Lenses, Devices, Systems and Methods for Refractive Error

ABSTRACT

The present disclosure is directed to lenses, devices, methods and/or systems for addressing refractive error. Certain embodiments are directed to changing or controlling the wavefront of the light entering a human eye. The lenses, devices, methods and/or systems can be used for correcting, addressing, mitigating or treating refractive errors and provide excellent vision at distances encompassing far to near without significant ghosting. The refractive error may for example arise from myopia, hyperopia, or presbyopia with or without astigmatism. Certain disclosed embodiments of lenses, devices and/or methods include embodiments that address foveal and/or peripheral vision. Exemplary of lenses in the fields of certain embodiments include contact lenses, corneal onlays, corneal inlays, and lenses for intraocular devices both anterior and posterior chamber, accommodating intraocular lenses, electro-active spectacle lenses and/or refractive surgery.

CROSS REFERENCE TO RELATED MATERIALS

This application is a continuation of U.S. application Ser. No.14/884,533, entitled Lenses, Devices, Systems and Methods for RefractiveError, filed 15 Oct. 2015, which is a continuation of U.S. applicationSer. No. 14/046,356, entitled Lenses, Devices, Methods and Systems forRefractive Error, filed 4 Ocotober 2013, which is a continuation-in-partof PCT/AU2013/000354 entitled Lenses, Devices, Methods and Systems forRefractive Error, filed 5 Apr. 2013, and a continuation-in-part of U.S.application Ser. No. 13/857,613 entitled Lenses, Devices and Methods forOcular Refractive Error filed 5 Apr. 2013, and which claims priority toAustralian Patent Application No. 2013202694 entitled Lenses, Devices,Methods and Systems for Refractive Error, filed 5 Apr. 2013, andAustralian Provisional Application No. 2012/904,541 entitled Lenses,Devices and Methods for Ocular Refractive Error, filed 17 Oct. 2012.Each of these priority applications are incorporated herein by referencein their entirety. This application is also related to AustralianProvisional Application No. 2012/901,382, entitled “Devices and Methodsfor Refractive Error Control” filed on 5 Apr. 2012. This AustralianProvisional Application is incorporated herein by reference in itsentirety. In addition, U.S. Pat. Nos. 7,077,522 and 7,357,509 are eachincorporated herein by reference in their entirety.

FIELD

Certain disclosed embodiments include lenses, devices and/or methods forchanging or controlling the wavefront of light entering an eye, inparticular a human eye.

Certain disclosed embodiments are directed to the configuration oflenses, devices, methods and/or systems for correcting or treatingrefractive errors.

Certain disclosed embodiments are directed to the configuration oflenses, devices, methods and/or systems for addressing refractive errorswhile provide excellent vision from far to near without significantghosting.

Certain disclosed embodiments include lenses, devices and/or methods forcorrecting, treating, mitigating and/or addressing refractive error, inparticular in human eyes. The refractive error may for example arisefrom myopia or hyperopia, with or without astigmatism. The refractiveerror may arise from presbyopia, either alone or in combination withmyopia or hyperopia and with or without astigmatism.

Certain disclosed embodiments of lenses, devices and/or methods includeembodiments that address foveal vision; certain embodiments that addressboth foveal and peripheral vision; and certain other embodiments addressperipheral vision.

Exemplary of lenses in the fields of certain embodiments include contactlenses, corneal onlays, corneal inlays, and lenses for intraoculardevices (both anterior and posterior chamber).

Exemplary devices in the fields of certain disclosed embodiments includeaccommodating intraocular lenses and/or electro-active spectacle lenses.

Exemplary methods in the fields of certain embodiments include methodsof changing the refractive state and/or wavefront of light entering aneye and received by a retina of the eye (e.g. refractive surgery,corneal ablation), methods of design and/or manufacture of lenses andoptical devices, methods of surgery to alter the refractive state of aneye and methods of controlling stimulus for progression of eye growth.

BACKGROUND

For an image to be perceived clearly, the optics of the eye shouldresult in an image that is focussed on the retina. Myopia, commonlyknown as short-sightedness, is an optical disorder of the eye whereinon-axis images are focussed in front of the fovea of the retina.Hyperopia, commonly known as long-sightedness, is an optical disorder ofthe eye wherein on-axis images are focussed behind the fovea of theretina. The focussing of images in front of or behind the fovea of theretina creates a lower order aberration of defocus. Another lower orderaberration is astigmatism. An eye may also have higher order opticalaberrations, including, for example, spherical aberration, coma and/ortrefoil. Many people experiencing natural refractive error areprogressing (the refractive error is increasing over time). Progressionis particularly widespread in people with myopia.

Schematic representations of eyes exhibiting myopia or hyperopia andastigmatism are shown in FIGS. 1A-C respectively. In a myopic eye 100,the parallel incoming beam of light 102 passes the refractive elementsof the eye, namely, the cornea 104 and crystalline lens 106, to a focalpoint 108 short of the retina 110. The image on the retina 110 istherefore blurred. In a hyperopic eye 120, the parallel incoming beam oflight 122 passes the refractive elements of the eye, namely, the cornea124 and crystalline lens 126, to a focal point 128 beyond the retina130, again rendering the image on the retina 130 blurred. In anastigmatic eye 140, the parallel incoming beam of light 142 passes therefractive elements of the eye, namely, cornea 144 and crystalline lens146, and results in two foci, namely tangential 148 and sagittal 158foci. In the example of astigmatism shown in FIG. 1C, the tangentialfocus 148 is in front the retina 160 while the sagittal focus 158 isbehind the retina 160. The image on the retina in the astigmatic case isreferred to as circle of least confusion 160.

At birth human eyes are generally hyperopic, i.e. the axial length ofthe eyeball is too short for its optical power. With age, from infancyto adulthood, the eyeball continues to grow until its refractive statestabilizes. Elongation of the eye in a growing human may be controlledby a feedback mechanism, known as the emmetropisation process, so thatthe position of focus relative to the retina plays a role in controllingthe extent of eye growth. Deviation from this process would potentiallyresult in refractive disorders like myopia, hyperopia and/orastigmatism. While there is ongoing research into the cause of deviationof emmetropisation from stabilising at emmetropia, one theory is thatoptical feedback can provide a part in controlling eye growth. Forexample, FIG. 2 shows cases that would, under a feedback mechanismtheory of the emmetropisation process, alter the emmetropisationprocess. In FIG. 2A, the parallel incoming beam of light 202 passesthrough a negative refractive element 203 and the refractive elements ofthe eye (the cornea 204 and crystalline lens 206), to form an image atfocus point 208, overshooting the retina 210. The resulting image bluron the retina, called hyperopic defocus, is an example of defocus thatmay encourage eye growth under this feedback mechanism. In contrast, asseen in FIG. 2B, the parallel incoming beam of light 252 passes througha positive refractive element 253, the refractive elements of the eye(cornea 254 and crystalline lens 256) to form an image at focus point258 in front of the retina 260. The resulting image blur, called myopicdefocus, on this retina is considered to be an example of defocusinduced at the retina that would not encourage eye growth. Therefore, ithas been proposed that progression of myopic refractive error can becontrolled by positioning of the focus in front of the retina. For anastigmatic system, the spherical equivalent, i.e. the mid-point betweenthe tangential and sagittal foci, may be positioned in front of theretina. These proposals have not however provided a full explanation orsolution, particularly in the case of progressing myopia.

A number of optical device designs and refractive surgery methods havebeen proposed to control the growth of the eye during emmetropisation.Many are generally based on refinements to the idea summarised abovethat foveal imagery provides a stimulus that controls the growth of theeye. In humans, the eye grows longer during emmetropisation and cannotgrow shorter. Accordingly, during emmetropisation an eye may grow longerto correct for hyperopia, but it cannot grow shorter to correct formyopia. Proposals have been made for addressing myopia progression.

In addition to proposed optical strategies to counter the development ofrefractive error and its progression, in particular myopia, there hasalso been interest in strategies that involve non-optical interventionlike pharmacological substances, such as atropine or pirenzipine.

Another condition of the eye is presbyopia, in which the eye's abilityto accommodate is reduced or the eye has lost its ability toaccommodate. Presbyopia may be experienced in combination with myopia,hyperopia, astigmatism and higher order aberrations. Different methods,devices and lenses to address presbyopia have been proposed, includingin the form of bifocal, multifocal or progressive additionlenses/devices, which simultaneously provide two or more foci to theeye. Common types of lenses used for presbyopia include the following:single vision reading glasses, bifocal or multifocal spectacles;centre-near or centre-distance bifocal and multifocal contact lenses,concentric (ring-type) bifocal contact lenses or multifocal intraocularlenses.

In addition, on occasion it is necessary to remove the crystalline lensof an eye, for example if the person is suffering from cataracts. Theremoved natural crystalline lens may be replaced by an intraocular lens.Accommodating intraocular lenses allow the eye to control the refractivepower of the lens, for example through haptics extending from the lensto the ciliary body.

Masking has been proposed as a way to improve the depth of focus of theeye. However, masking results in loss of light to the eye which is anundesirable quality as it at least deteriorates the contrast of theimages cast on the retina. In addition, these features are a challengeto implement on lenses for example, contact and/or intra ocular lenses.

Some problems with existing lenses, devices, methods and/or systems arethat, for example, they attempt to correct refractive errors butcompromise the quality of the vision at different distances and/orintroduce ghosting and/or distortion. Accordingly, what is needed arelenses, devices, methods and/or systems for mitigating and/or addressingrefractive errors, for example, myopia, hyperopia or presbyopia, with orwithout astigmatism, without causing at least one or more of theshortcomings discussed herein. Other solutions will become apparent asdiscussed herein.

SUMMARY

Certain embodiments are directed to various lenses, devices and/ormethods for providing an aberration profile for an eye. Characteristicsof aberration profiles and/or methodologies for identifying aberrationprofiles are described for myopic eyes, hyperopic eyes and/or presbyopiceyes. In addition lenses, devices and methods for an eye withastigmatism are disclosed.

In certain embodiments, a lens for an eye has an optical axis and anaberration profile about its optical axis, the aberration profile havinga focal distance and including at least one of a primary sphericalaberration component C(4,0) and a secondary spherical aberrationcomponent C(6,0). The aberration profile provides a retinal imagequality (RIQ) with a through focus slope that degrades in a direction ofeye growth; and a RIQ of at least 0.3. The RIQ is visual Strehl Ratiomeasured along the optical axis for at least one pupil diameter in therange 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive. In other embodiments the RIQ measuremay be different, for example, in some embodiments the RIQ measure maybe from one of the following: a simple Strehl ratio in spatial domain, asimple Strehl ratio in frequency domain, a visual Strehl ratio withinclusion of cosine of phase transfer function, a visual Strehl ratiowith weighted contrast sensitivity function, a multifocal benefit ratio,a metric obtained from a two dimensional correlation analysis in spatialdomain, a metric obtained from a two dimensional correlation analysis infrequency domain, or number of phase reversals in frequency domain.

In certain embodiments, a lens includes an optical axis and anaberration profile about the optical axis that provides a focal distancethat comprises a C(2,0) Zernike coefficient term; a peak visual StrehlRatio (‘first visual Strehl Ratio’) within a through focus range, and avisual Strehl Ratio that remains at or above a second visual StrehlRatio over the through focus range that includes said focal distance,wherein the visual Strehl Ratio is measured for at least one pupildiameter in the range 3 mm to 5 mm, over a spatial frequency range of 0to 30 cycles/degree inclusive, at a wavelength selected from within therange 540 nm to 590 nm inclusive, and wherein the first visual StrehlRatio is at least 0.35, the second visual Strehl Ratio is at least 0.10and the through focus range is at least 1.8 Dioptres.

In certain embodiments, a lens comprises an optical axis and anaberration profile about the optical axis that provides a focal distancethat comprises a C(2,0) Zernike coefficient term; a peak RIQ (‘firstRIQ) within a through focus range, and a RIQ that remains at or above asecond RIQ over the through focus range that comprises said focaldistance, wherein the RIQ is visual Strehl Ratio with inclusion ofcosine of the phase transfer function measured for at least one pupildiameter in the range 3 mm to 5 mm, over a spatial frequency range of 0to 30 cycles/degree inclusive, at a wavelength selected from within therange 540 nm to 590 nm inclusive, and wherein the first RIQ is at least0.3, the second visual Strehl Ratio is at least 0.10 and the throughfocus range is at least 1.8 Dioptres. In other embodiments the RIQmeasure may be different, for example, in some embodiments the RIQmeasure may be from one of the following: a simple Strehl ratio inspatial domain, a simple Strehl ratio in frequency domain, a visualStrehl ratio in spatial domain, a visual Strehl ratio in frequencydomain, a visual Strehl ratio with weighted contrast sensitivityfunction, a multifocal benefit ratio, a metric obtained from a twodimensional correlation analysis in spatial domain, a metric obtainedfrom a two dimensional correlation analysis in frequency domain, ornumber of phase reversals in frequency domain. In certain embodiments, amethod for a presbyopic eye includes identifying a wavefront aberrationprofile for the eye, the wavefront aberration profile including at leasttwo spherical aberration terms greater than C(4,0). The prescriptionfocal distance of the aberration profile is determined taking intoaccount said spherical aberration and wherein the prescription focaldistance is at least +0.25 D relative to a focal distance for a C(2,0)Zernike coefficient term of the wavefront aberration profile. The methodmay include producing a device, lens and/or corneal profile for the eyeto affect said wavefront aberration profile.

In certain embodiments, a method for a myopic eye includes identifying awavefront aberration profile for the eye and applying or prescribing theaberration profile. The wavefront aberration profile includes at leasttwo spherical aberration terms, wherein the prescription focal distanceof the aberration profile is determined taking into account saidspherical aberration and wherein the prescription focal distance is atleast +0.10 D relative to a focal distance for a C(2,0) Zernikecoefficient term of the wavefront aberration profile. The wavefrontaberration profile also provides a degrading retinal image quality inthe direction posterior to the retina.

Certain embodiments are directed to, a method for a hyperopic eye, themethod comprising identifying a wavefront aberration profile for the eyeand applying or prescribing the aberration profile. The wavefrontaberration profile includes at least two spherical aberration terms,wherein the prescription focal distance of the wavefront aberrationprofile is determined taking into account said spherical aberration. Atthe prescription focal distance the wavefront aberration profileprovides an improving retinal image quality in the direction posteriorto the retina.

In certain embodiments a computational device includes an input toreceive first combination of aberrations, one or more processors tocompute a second combination of aberrations for one or more opticalsurfaces, and an output to output the second combination of aberrations,wherein the computed second combination of aberrations provides incombination with the first combination of aberrations a totalcombination of higher order aberrations (HOA) as disclosed herein. Incertain embodiments, the computational device may be used to generatepower profiles, aberration profiles, wavefront ablation profiles orcombinations thereof. These computations may then be used for contactlenses, corneal inlays, corneal onlays, single and dual elementintra-ocular lenses anterior and/or posterior chamber, accommodativeintra-ocular lenses, wavefront ablation for corneal refractive surgerytechniques and other suitable devices and/or applications.

The aberration profiles disclosed herein may be used over the optic zoneof the lens, a portion of the optic zone of the lens or a substantialportion of the optic zone of the lens. How much of the optic zones ofthe lens that involves the aberration profile may depend on a particularapplication of the embodiments disclosed. In certain applications, theaberration profiles disclosed herein may be used over at least two,three or four portions of the optical zone of the lens. These multipleportions may be discrete portions, overlapping portions or combinationsthereof. The multiple portions of the aberration used over one or moreportions of the optic zone of the lens may have the same aberration orpower profiles, substantially the same aberration or power profiles,different aberration or power profiles or combinations thereof. Incertain embodiments, the aberration profiles disclosed herein may beused over at least 10%, 20%, 30%, 40% or 50% of the optical zone of thelens. In certain embodiments, the aberration profiles and or powerprofiles disclosed herein may be used over between 5% to 10%, 5% to 30%,5%, to 50%, 5% to 75%, 5% to 95%, 50% to 95% or 60% to 99% of theoptical zone of the lens.

A lens for an eye, the lens comprising: an optical axis and anaberration profile associated with the optical axis; and a focaldistance; wherein the aberration profile comprises four or more higherorder aberrations; wherein the lens is configured to provide visualperformance over near, intermediate and far distances that is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance and to provideminimal ghosting at far, intermediate and near distances; wherein thelens is also configured to provide a Strehl ratio of at least 0.2 at thefocal distance and to provide a through-focus slope of the Strehl ratiothat degrades in a negative power end of the through-focus range; andwherein the Strehl Ratio is measured substantially along the opticalaxis for at least a portion of the optic zone diameter in the range 3 mmto 6 mm, over a spatial frequency range of 0 to 30 cycles/degreeinclusive and at a wavelength selected from within the range 540 nm to590 nm inclusive.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting through-focus retinal imagequality have inter alias the advantage that they provide minimalghosting at various distances from far, intermediate and near.

In certain embodiments, the described and/or claimed specific at leastthree higher order aberration terms and the resulting through-focusretinal image quality have inter alias the advantage that they provideminimal ghosting at various distances from far, intermediate and near.

In certain embodiments, the described and/or claimed specific at leastfour higher order aberration terms and the resulting through-focusretinal image quality have inter alias the advantage that they provideminimal ghosting at various distances from far, intermediate and near.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting through-focus retinal imagequality have inter alias the advantage that they provide improved visionat various distances from far, intermediate and near.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting through-focus retinal imagequality have inter alias the advantage that they provide improved visionand minimise ghosting at various distances from far, intermediate andnear.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting RIQ of at least 0.3 and thethrough focus RIQ slope that degrades in a direction of eye growth, haveinter alias the advantage that they provide minimal ghosting at variousdistances from far, intermediate and near and have a potential to reducethe progression of myopia.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting RIQ of at least 0.3 and thethrough focus RIQ slope that improves in a direction of eye growth, haveinter alias the advantage that they provide minimal ghosting at variousdistances from far, intermediate and near and have a potentialcorrection for hyperopia.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles including at least four spherical aberrationterms selected from the group C(4,0) to C(20,0) have inter alias theadvantage that they provide lenses that improve vision and minimiseghosting at various distances from far, intermediate and near and have apotential correction for hyperopia.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting in the first visual StrehlRatio is at least 0.35, the second visual Strehl Ratio is at least 0.1and the through focus range is at least 1.8 D, have inter alias theadvantage that they provide improved vision at distances ranging fromfar and intermediate, and/or provide minimal ghosting at distancesranging from far and intermediate.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting in the first visual StrehlRatio is at least 0.35, the second visual Strehl Ratio is at least 0.1and the through focus range is at least 2.25 D, have inter alias theadvantage that they provide improved vision at distances ranging fromfar, intermediate and near, and/or provide minimal ghosting at distancesranging from far, intermediate and near.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting retinal image quality inmultifocal lenses have inter alias the advantage that they provide avisual performance over intermediate and far distances that is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance; and isconfigured to provide minimal ghosting at far, intermediate and neardistances.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting through-focus retinal imagequality have inter alias the advantage that they provide minimalghosting at various distances from far, intermediate and near.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles and the resulting through-focus retinal imagequality have inter alias the advantage that they provide minimalghosting at various distances from far and intermediate.

In certain embodiments, the described and/or claimed specific two ormore higher order aberrations having one or more of the followingcomponents: a primary spherical aberration C(4,0), a secondary sphericalaberration C(6,0), a tertiary spherical aberration C(8,0), a quaternaryspherical aberration C(10,0), a pentanary spherical aberration C(12,0),a hexanary spherical aberration C(14,0), a heptanary sphericalaberration C(16,0), an octanary spherical aberration C(18,0) and ananonary spherical aberration C(20,0) and the resulting through focusslope of the visual Strehl ratio so that the slope visual Strehl ratiodecreases in a direction of eye growth, have inter alias the advantagethat they provide improved vision at far distance, minimal ghosting andhave a potential to reduce the progression of myopia.

In certain embodiments, the described and/or claimed specific aberrationprofiles that is comprised of at least two spherical aberration termsand a defocus term have inter alias the advantage that they provide inlenses a visual performance at the near visual distance that is withintwo units of the visual performance of the appropriately prescribedsingle-vision lens at far distance.

In certain embodiments, the described and/or claimed specific aberrationprofiles that is comprised of at least two spherical aberration termsand a defocus term have inter alias the advantage that they providemultifocal lenses with a visual performance on a visual analogue scaleat a near visual distance has a score of 9 or above in 25%, 30%, 35%,40%, 45%, 50% or 55% of a representative sample of presbyopes.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles selected at least in part from a groupcomprising spherical aberration coefficients from C(4,0) to C(20,0),have inter alias the advantage that they provide correction ofastigmatism up to 1 Dioptre without substantial use of rotationallystable toric lens design features.

In certain embodiments, the described and/or claimed specific higherorder aberration profiles selected at least in part from a groupcomprising spherical aberration coefficients from C(4,0) to C(20,0),have inter alias the advantage that they provide expansion of thedepth-of-focus of the eye by altering the retinal image quality over arange of distances.

In certain embodiments, the described and/or claimed intra-ocular lenssystems with a first lens, a second lens and at least three higher orderaberration terms have inter alias the advantage that they provideimproved vision along a range of substantially continuous visualdistances, including near, intermediate and far distances that issubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance.

In certain embodiments, the described and/or claimed power profiles witha transition between a maxima and a minima, and the maxima is within 0.2mm of the centre of the optic zone and the minima is less than or equalto 0.3, 0.6, 0.9 or 1 mm distance from the maxima and the amplitude ofthe transition between the maxima and the minima is at least 2.5D, 4D,5D, or 6D have inter alias the advantage that they provide a lens thatis configured to provide a visual performance over intermediate and fardistances that is at least substantially equivalent to the visualperformance of a correctly prescribed single-vision lens at the farvisual distance and the lens is configured to provide minimal ghostingat far, intermediate and near distances.

Further embodiments and or advantages of one or more embodiments willbecome apparent from the following description, given by way of exampleand with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the presentdisclosure will become better understood with regard to the followingdescription, appended claims, and accompanying figures.

FIG. 1, including FIGS. 1A-1C, are schematic representations of eyesexhibiting myopia, hyperopia and astigmatism respectively.

FIG. 2, including FIGS. 2A and 2B, are schematic representationsrespectively of hyperopic defocus and myopic defocus induced at theretina.

FIG. 3 shows a two-dimensional through-focus point spread functioncomputed at the retinal plane without higher order aberrations (HOA) andin the presence of HOA of spherical aberration, vertical coma andhorizontal trefoil, according to certain embodiments.

FIGS. 4 to 7 show graphs of the interaction of primary sphericalaberration with horizontal coma, vertical coma, horizontal trefoil andvertical trefoil respectively, according to certain embodiments.

FIG. 8 shows a graph indicating the magnitude of myopia progressionunder an optical feedback mechanism for eye growth, for primaryspherical aberration vs. primary vertical astigmatism vs. primaryhorizontal astigmatism, according to certain embodiments.

FIG. 9 shows a graph indicating the magnitude of myopia progression forprimary spherical aberration vs. secondary vertical astigmatism vs.secondary horizontal astigmatism, according to certain embodiments.

FIG. 10 shows a graph indicating the myopia progression on a binaryscale for primary spherical aberration vs. secondary sphericalaberration, according to certain embodiments.

FIG. 11 shows a graph indicating the myopia progression on a binaryscale for primary spherical aberration vs. tertiary sphericalaberration, according to certain embodiments.

FIG. 12 shows a graph indicating the myopia progression on a binaryscale for primary spherical aberration vs. quaternary sphericalaberration, according to certain embodiments.

FIG. 13 shows a graph indicating the myopia progression on a binaryscale for primary spherical aberration vs. secondary sphericalaberration vs. tertiary spherical aberration, according to certainembodiments.

FIG. 14 shows example designs of aberration profiles that providenegative and positive gradient RIQ in a direction of eye growth,according to certain embodiments.

FIG. 15 shows a work flow chart for myopic eyes, progressing ornon-progressing, according to certain embodiments.

FIG. 16 shows a work flow chart for hyperopic eyes, progressing ornon-progressing towards emmetropia, according to certain embodiments.

FIGS. 17 to 25 show example designs of power profiles of correcting lensacross the optic zone diameter, for affecting optical feedbackmechanisms for myopia, according to certain embodiments.

FIG. 26 shows an example design of a power profile of correcting lensacross the optic zone diameter, for affecting optical feedbackmechanisms for hyperopia, according to certain embodiments.

FIG. 27 shows a global through-focus retinal image quality (TFRIQ) foran aberration profile corresponding to a single vision lens.

FIG. 28 shows a global TFRIQ for a first aberration profile (IterationA1), which may have application to a progressing myopic eye.

FIG. 29 shows the power profile for a lens for providing the firstaberration profile (Iteration A1), according to certain embodiments.

FIG. 30 shows a global TFRIQ for a second aberration profile (IterationA2), which may also have application to a progressing myopic eye,according to certain embodiments.

FIG. 31 shows the power profile across full chord diameter for a secondaberration profile (Iteration A2), according to certain embodiments.

FIGS. 32 and 33 show a global TFRIQ for a third and fourth aberrationprofile (Iteration C1 and Iteration C2 represented as power profilesacross optic chord diameter in FIGS. 34 and 35), which may haveapplication to a hyperopic eye, according to certain embodiments.

FIG. 34 shows a power profile for a lens for providing the thirdaberration profile (Iteration C1) according to certain embodiments.

FIG. 35 shows a power profile for a lens for providing the fourthaberration profile (Iteration C2) according to certain embodiments.

FIG. 36 shows a retinal image quality (RIQ) for seven aberrationprofiles over a through focus range of 2.5D. The seven aberrationprofiles correspond to example centre-distance and centre-near asphericmultifocals and concentric ring/annulus type bifocals and threeexemplary aberration profiles (Iteration B1, Iteration B2, Iteration B3)obtained after optimising through focus performance, according tocertain embodiments.

FIGS. 37 to 43 show the power profiles of contact lenses across theoptic zone diameter, for providing the TFRIQ described in FIG. 36,according to certain embodiments.

FIGS. 44 to 46 show the on-axis TFRIQ for the three exemplaryembodiments for presbyopia (Iteration B1, B2 and B3) across four pupildiameters (3 mm to 6 mm).

FIGS. 47 and 48 show the on-axis TFRIQ for the centre-distance andcentre-near concentric designs across four pupil diameters (3 mm to 6mm), according to certain embodiments.

FIGS. 49 and 50 show the on-axis TFRIQ for the centre-distance andcentre-near aspheric multifocal designs across four pupil diameters (3mm to 6 mm), according to certain embodiments.

FIGS. 51 and 52 show a monocular correction approach for presbyopia,where different higher order aberration profiles provided for the rightand left eyes, by which the through-focus optical and/or visualperformance is different in the right and left eye (desired vergences)to provide a combined add power range of 1.5D and 2.5D, on the negativeside of through-focus curve, respectively, according to certainembodiments.

FIGS. 53 and 54 show a monocular correction approach for presbyopia,where different higher order aberration profiles provided for the rightand left eyes, by which the through-focus optical and/or visualperformance is different in the right and left eye (desired vergences)to provide a combined add power range of 1.5D and 2.5D, on the positiveside of through-focus curve, respectively, according to certainembodiments.

FIG. 55 shows a global TFRIQ for three further iterations of aberrationprofile (Iterations A3, A4 and A5 represented in FIGS. 56, 57 and 58,respectively), for providing a substantially constant retinal imagequality across a horizontal visual field from 0 to 30 degrees, accordingto certain embodiments.

FIG. 56 shows a power profile for a lens for providing anotheraberration profile (Iteration A3) according to certain embodiments.

FIG. 57 shows a power profile for a lens for providing anotheraberration profile (Iteration A4) according to certain embodiments.

FIG. 58 shows a power profile for a lens for providing anotheraberration profile (Iteration A5) according to certain embodiments.

FIGS. 59 and 60 show example designs of the power profile of correctingcontact lenses with opposite phase profiles (Iteration E1 and IterationE2.

FIGS. 61 to 63 show the on-axis TFRIQ for Iterations E1 and E2 withthree different levels of inherent primary spherical aberration of thecandidate eye, according to certain embodiments.

FIG. 64 shows the TFRIQ performance measures (depth of focus) of 78exemplary aberration profiles (Appendix A) that involve a combination ofspherical aberration terms. The Y-axis in the graph denotes ‘Q’performance metric and X-axis denotes the through-focus range from −1.5to +1D. In this exemplary, the calculations were performed at 4 mmpupil. The solid black line indicates the through-focus performance of acombination that does not have a mode of spherical aberration while thegrey lines indicate the 78 combinations which include at least onehigher order spherical aberration term. The 78 combinations wereselected with regard to performance on the negative side of thethrough-focus curve, according to certain embodiments.

FIG. 65 shows the TFRIQ performance of one exemplary combination fromFIG. 56 that involves only positive spherical aberration in comparisonwith a combination that has no spherical aberration, according tocertain embodiments.

FIG. 66 shows the TFRIQ performance measures (depth of focus) of 67exemplary aberration profiles that involve a combination of sphericalaberration terms (Appendix C). The Y-axis in the graph denotes ‘Q’performance metric and X-axis denotes the through-focus range from −1.5to +1D. In this exemplary, the calculations were performed at 4 mmpupil. The solid black line indicates the through-focus performance of acombination that does not have a mode of spherical aberration while thegrey lines indicate the 67 combinations which include at least onehigher order spherical aberration term. These 67 combinations improveperformance on the positive side of the through-focus curve, accordingto certain embodiments.

FIG. 67 shows a work flow chart for presbyopic eyes, according tocertain embodiments.

FIG. 68 shows a power profile for a toric prescription of a contact lensfor both astigmatism and presbyopia, according to certain embodiments.

FIG. 69 shows an example lens power profile, which is availed from anexemplary combination of spherical aberration terms.

FIG. 70 shows the lens power profile converted to an axial thicknessprofile for a contact lens, according to certain embodiments.

FIG. 71 shows an example of axial power profile of lens across acomplete chord diameter (Iteration G1), which is one exemplary of designset whose performance is substantially independent of inherent sphericalaberration of the candidate eye, according to certain embodiments.

FIG. 72 shows the TFRIQ of an exemplary, described as Iteration G1, at 4mm pupil diameter. Y-axis denotes RIQ performance metric and X-axisdenotes through-focus range from −1D to +1.75D. The four differentlegends, solid black line, solid grey line, dashed black like and, soliddouble line represent four different levels of spherical aberration in asample of the affected population at 5 mm pupil diameter, according tocertain embodiments.

FIG. 73 shows the TFRIQ of an exemplary, described as Iteration G1, at a5 mm pupil diameter. Y-axis denotes RIQ performance metric and X-axisdenotes through-focus range from −1D to +1.75D. The four differentlegends, solid black line, solid grey line, dashed black like and, soliddouble line represent four different levels of spherical aberration in asample of the affected population, at 5 mm pupil diameter, according tocertain embodiments.

FIG. 74 shows an example of axial power profile of a lens across ahalf-chord diameter (Iteration J1), which is one exemplary of design setfor an intra-ocular lens used to restore vision at distances,encompassing far to near, after removal of the crystalline lens in theeye, according to certain embodiments.

FIG. 75 shows an example of axial thickness profile of a lens (IterationJ1) across a half-chord diameter, which is one exemplary of design setfor an intra-ocular lens used to restore vision at distances,encompassing from far to near, after removal of the crystalline lens inthe eye, according to certain embodiments.

FIG. 76 show power profiles of eleven different contact lenses across ahalf-chord diameter, these eleven different designs (Iterations K1 toK11). These are some designs of commercial available lenses.

FIG. 77 show power profiles of four different lenses across a half-chorddiameter, these four different designs (Iterations R1 to R4) areexemplary of certain embodiments.

FIG. 78 show the normalised absolute of amplitude spectrum of a FastFourier Transform of eleven different contact lenses (Iterations K1 toK11) as a function of spatial frequency in Cycles/mm. These are theeleven lenses presented in FIG. 76.

FIG. 79 show the normalised absolute of amplitude spectrum of a FastFourier Transform of four different lens designs (Iterations R1 to R4)as a function of spatial frequency in Cycles/mm. These four designs areexemplary of certain embodiments.

FIG. 80 show the absolute first derivative of eleven different contactlenses (Iteration K1 to K11) as a function of half-chord diameter (mm).These are the eleven lenses presented in FIG. 76.

FIG. 81 show the absolute first derivative of four different contactlenses (Iteration R1 to R4) as a function of half-chord diameter (mm).These four designs are exemplary of certain embodiments.

FIG. 82 show the average subjective ratings measured on a visualanalogue scale for distance vision for a sample of an affectedpresbyopic population. Four of the lenses H to K are exemplary ofcertain embodiments, while lenses A to G are commercial lenses.

FIG. 83 show the average subjective ratings measured on a visualanalogue scale for intermediate vision for a sample of an affectedpresbyopic population. Four of the lenses H to K are exemplary ofcertain embodiments, while lenses A to G are commercial lenses.

FIG. 84 show the average subjective ratings measured on a visualanalogue scale for near vision for a sample of an affected presbyopicpopulation. Four of the lenses H to K are exemplary of certainembodiments, while lenses A to G are commercial lenses

FIG. 85 show the average subjective ratings measured on a ghostinganalogue scale for distance vision for a sample of an affectedpresbyopic population. Four of the lenses H to K are exemplary ofcertain embodiments, while lenses A to G are commercial lenses.

FIG. 86 show the average subjective ratings measured on a ghostinganalogue scale for near vision for a sample of an affected presbyopicpopulation. Four of the lenses H to K are exemplary of certainembodiments, while lenses A to G are commercial lenses.

FIG. 87 show the average subjective ratings measured on a visualanalogue scale for overall vision for a sample of an affected presbyopicpopulation. Four of the lenses H to K are exemplary of certainembodiments, while lenses A to G are commercial lenses.

FIG. 88 show the average subjective ratings measured on a lack ofghosting analogue scale for distance vision for a sample of an affectedpresbyopic population. Four of the lenses H to K are exemplary ofcertain embodiments, while lenses A to G are commercial lenses.

FIG. 89 show the average subjective ratings measured on a lack ofghosting analogue scale for near vision for a sample of an affectedpresbyopic population. Four of the lenses H to K are exemplary ofcertain embodiments, while lenses A to G are commercial lenses.

FIG. 90 show the average subjective ratings measured on a ghostinganalogue scale for distance and near vision combined for a sample of anaffected presbyopic population. Four of the lenses H to K are exemplaryof certain embodiments, while lenses A to G are commercial lenses.

FIG. 91 show the average subjective ratings measured on a visualanalogue scale for cumulative performance of vision including distance,intermediate, near vision and lack of ghosting at distance and near fora sample of an affected presbyopic population. Four of the lenses H to Kare exemplary of certain embodiments, while lenses A to G are commerciallenses.

FIG. 92 shows the percentage of people whose subjective rating score ona visual analogue scale was greater than 9, for distance vision. Thedata were obtained from a sample of an affected presbyopic population.Four of the lenses H to K are exemplary of certain embodiments, whilelenses A to G are commercial lenses.

FIG. 93 shows the percentage of people whose subjective rating score ona visual analogue scale was greater than 9, for intermediate vision. Thedata were obtained from a sample of an affected presbyopic population.Four of the lenses H to K are exemplary of certain embodiments, whilelenses A to G are commercial lenses.

FIG. 94 shows the percentage of people whose subjective rating score ona visual analogue scale was greater than 9, for near vision. The datawere obtained from a sample of an affected presbyopic population. Fourof the lenses H to K are exemplary of certain embodiments, while lensesA to G are commercial lenses.

FIG. 95 shows the percentage of people whose subjective rating score ona visual analogue scale was greater than 9, for overall vision. The datawere obtained from a sample of an affected presbyopic population. Fourof the lenses H to K are exemplary of certain embodiments, while lensesA to G are commercial lenses.

FIG. 96 shows the percentage of people whose subjective rating score ona ghosting analogue scale was greater than 3, for distance vision. Thedata were obtained from a sample of an affected presbyopic population.Four of the lenses H to K are exemplary of certain embodiments, whilelenses A to G are commercial lenses.

FIG. 97 shows the percentage of people whose subjective rating score ona ghosting analogue scale was greater than 3, for near vision. The datawere obtained from a sample of an affected presbyopic population. Fourof the lenses H to K are exemplary of certain embodiments, while lensesA to G are commercial lenses.

FIG. 98 shows the percentage of people whose subjective rating score ona visual analogue scale was greater than 9, for cumulative vision. Thecumulative vision rating was obtained by averaging the distance,intermediate, near, overall vision ratings, also including lack ofghosting for distance and near. The data were obtained from a sample ofan affected presbyopic population. Four of the lenses H to K areexemplary of certain embodiments, while lenses A to G are commerciallenses.

FIG. 99 shows the average objective measures of high-contrast visualacuity on a sample of an affected presbyopic population. The measureswere obtained using a test distance of 6 metres and presented in log MARscale. Four of the lenses H to K are exemplary of certain embodiments,while lenses A to G are commercial lenses.

FIG. 100 shows the average objective measures of contrast sensitivity ona sample of an affected presbyopic population. The measures wereobtained using a test distance of 6 metres and presented in log scale.Four of the lenses H to K are exemplary of certain embodiments, whilelenses A to G are commercial lenses.

FIG. 101 shows the average objective measures of low-contrast visualacuity on a sample of an affected presbyopic population. The measureswere obtained using a test distance of 6 metres and presented in log MARscale. Four of the lenses H to K are exemplary of certain embodiments,while lenses A to G are commercial lenses.

FIG. 102 shows the average objective measures of intermediate visualacuity on a sample of an affected presbyopic population, using a testdistance of 70 centimetres. The measures are presented in log MAR scale.Four of the lenses H to K are exemplary of certain embodiments, whilelenses A to G are commercial lenses.

FIG. 103 shows the average objective measures of near visual acuity on asample of an affected presbyopic population, using a test distance of 50centimetres. The measures are presented in log MAR scale. Four of thelenses H to K are exemplary of certain embodiments, while lenses A to Gare commercial lenses.

FIG. 104 shows the average objective measures of near visual acuity on asample of an affected presbyopic population, using a test distance of 40centimetres. The measures are presented in log MAR scale. Four of thelenses H to K are exemplary of certain embodiments, while lenses A to Gare commercial lenses.

FIG. 105 shows the average objective measures of combined visual acuityon a sample of an affected presbyopic population. The combined visualacuity includes measures at distance, intermediate and near at 50 cm.The measures are presented in log MAR scale. Four of the lenses H to Kare exemplary of certain embodiments, while lenses A to G are commerciallenses.

FIG. 106 shows the average objective measures of combined visual acuityon a sample of an affected presbyopic population. The combined visualacuity includes measures at distance, intermediate, near at 50 cm andnear at 50 cm. The measures are presented in log MAR scale. Four of thelenses H to K are exemplary of certain embodiments, while lenses A to Gare commercial lenses.

FIG. 107 shows the percentage of people whose subjective rating score ona visual analogue scale was equal to 1, for ghosting at distance ornear. The data were obtained from a sample of an affected presbyopicpopulation. Four of the lenses H to K are exemplary of certainembodiments, while lenses A to G are commercial lenses.

FIG. 108 shows the percentage of people whose subjective rating score ona visual analogue scale was less than 2, for ghosting at distance andnear. The data were obtained from a sample of an affected presbyopicpopulation. Four of the lenses H to K are exemplary of certainembodiments, while lenses A to G are commercial lenses.

FIG. 109 shows power profiles of three exemplary embodiments across thehalf-chord diameter. The power profiles of the three designs start atabout 3D at the centre and gradually ramp down to 0D power at 0.5, 0.75and 1 mm half-chord diameters.

FIG. 110 show the real-part of the optical transfer function (for a 4 mmoptic zone diameter) as a function of spatial frequencies for the lensesprofiles disclosed in FIG. 109. The neural contrast sensitivity functionis also plotted as a function of spatial frequencies to facilitategauging the impact of the designed plus power in the centre of the lenson the optical transfer function.

FIG. 111 shows power profiles of three exemplary embodiments across thehalf-chord diameter. The power profiles of the three designs start atabout 6D at the centre and gradually ramp down to 0D power at 0.5, 0.75and 1 mm half-chord diameters.

FIG. 112 show the real-part of the optical transfer function (for a 4 mmpupil diameter) as a function of spatial frequencies for the lensesprofiles disclosed in FIG. 111. The neural contrast sensitivity functionis also plotted as a function of spatial frequencies to facilitategauging the impact of the designed plus power in the centre of the lenson the optical transfer function.

FIG. 113 shows the power profiles of three exemplary embodiments acrossthe half-chord diameter. The power profiles of the three designs startat about 10D at the centre and gradually ramp down to 0D power at 0.5,0.75 and 1 mm half-chord diameters.

FIG. 114 shows the real-part of the optical transfer function (for a 4mm pupil diameter) as a function of spatial frequencies for the lensesprofiles disclosed in FIG. 114. The neural contrast sensitivity functionis also plotted as a function of spatial frequencies to facilitategauging the impact of the designed plus power in the centre of the lenson the optical transfer function.

FIG. 115 shows the power profiles of several exemplary embodimentsacross the half-chord diameter that have varying degrees of plus rangingfrom +3D to +7D in various zone widths ranging from 0.25 mm to 1 mm ofthe half-chord of the lens.

FIG. 116 plots the through-focus image quality (‘Q’ metric) for fiveexemplary combinations with higher order aberrations (T1 to T5) thatinclude symmetric higher order aberrations.

FIG. 117 shows the power profiles of two exemplary embodiments ofcontact lens designs (N41 and N42) across the half-chord diameter.

FIG. 118 plots the through-focus image quality (‘Q’ metric) for twoexemplary contact lenses (N41 and N42) calculated at 3 mm pupildiameter. The solid line and dual line represents the through-focusimage quality for two exemplary designs N41 and N42, one design is usedon one eye and the other design on the fellow eye. The dashed linerepresents the binocular performance.

FIGS. 119 to 123 show the measured power profiles of 10 commercialcontact lens designs across the half-chord diameter. These powerprofiles measurements were obtained on a commercial Hartmann-shack basedpower mapping system Optocraft (Optocraft Gmbh, Germany)

FIGS. 124 to 127 show the power profiles of 12 exemplary embodiments ofcontact lens designs across the half-chord diameter.

FIGS. 128 to 131 show the power profiles of 12 exemplary embodiments ofintra-ocular lens designs across the half-chord diameter.

FIG. 132 plots the through-focus image quality (‘Q’ metric) for eightexemplary example combinations of with higher order aberrations,including both symmetric and asymmetric higher order aberrations.

FIG. 133 plots the through-focus image quality (‘Q’ metric) for twoexemplary example combinations. The solid line with triangle symbolsrepresents the through-focus image quality obtained when −1.25 DC at 90degrees of astigmatism is combined with various levels of defocus. Thesolid line with circle symbols represents the through-focus imagequality when −1.25 DC at 90 degrees of astigmatism is combined with thehigher order aberration combination described in table 12.1 at variouslevels of defocus.

FIGS. 134 to 136 plots the real part of optical transfer function as afunction of spatial frequencies for three sets of exemplary aberrationcombinations. In these figures, the solid line represents the candidateeye with −1D of defocus with no other higher order aberrations, thedouble line represents the candidate eye when defocus is corrected andhigher order aberrations are left uncorrected. The triple linerepresents one set of higher order aberration combinations #1, #2 and #3described in tables 12.2.

FIG. 137 show the power profiles of two exemplary embodiments of contactlens designs (N11 and N12) across the half-chord diameter.

FIG. 138 plots the through-focus image quality (‘Q’ metric) for twoexemplary contact lens (N11 and N12) calculated at 3 mm pupil diameter.The solid line and dual line represents the through-focus image qualityfor two designs N11 and N12, when each design is used to correct a pairof eyes. The dashed line represents the binocular performance when boththe eyes work together in combination.

DETAILED DESCRIPTION

The present disclosure will now be described in detail with reference toone or more embodiments, some examples of which are illustrated and/orsupported in the accompanying figures. The examples and embodiments areprovided by way of explanation and are not to be taken as limiting tothe scope of the disclosure.

Furthermore, features illustrated or described as part of one embodimentmay be used by themselves to provide other embodiments and featuresillustrated or described as part of one embodiment may be used with oneor more other embodiments to provide a further embodiments. It will beunderstood that the present disclosure will cover these variations andembodiments as well as other variations and/or modifications.

It will be understood that the term “comprise” and any of itsderivatives (e.g., comprises, comprising) as used in this specificationis to be taken to be inclusive of features to which it refers, and isnot meant to exclude the presence of any additional features unlessotherwise stated or implied. The features disclosed in thisspecification (including accompanying claims, abstract, and drawings)may be replaced by alternative features serving the same, equivalent orsimilar purpose, unless expressly stated otherwise.

The subject headings used in the detailed description are included onlyfor the ease of reference of the reader and should not be used to limitthe subject matter found throughout the disclosure or the claims. Thesubject headings should not be used in construing the scope of theclaims or the claim limitations.

As defined herein, the term aberration profile may be an arrangement ofone or more aberrations in a one dimensional, a two dimensional or athree dimensional distribution. The arrangement may be continuous ordiscontinuous. Aberration profiles may be brought about by anarrangement of one or more power profiles, power patterns and powerdistributions in a one dimensional, a two dimensional or a threedimensional distribution. The arrangement may be continuous ordiscontinuous. Aberrations may be rotationally symmetric or asymmetric.

As used herein, the terms “across the range of dioptric distances” and“a range of dioptric distances” means a range of distances ascorresponding to equivalent units of dioptres. For example, a linearrange of distances from 100 cm to 50 cm corresponds to a range ofdioptric distances of 1D to 2D, respectively.

The optical and/or visual performance of the human eye may be limited byone or more optical and/or visual factors. Some of the factors mayinclude monochromatic and polychromatic optical wavefront aberrationsand the retinal sampling which may impose a Nyquist limit on spatialvision. Some other factors may include the Stiles-Crawford effect and/orscattering. These factors or combinations of these factors may be usedto determine retinal image quality (RIQ), according to certainembodiments. For example, retinal image quality (RIQ) may be obtained bymeasuring wavefront aberrations of the eye with or without a correctinglens in place using appropriate adjustments using factors such factorsas Stiles Crawford effect if required. As disclosed herein, various waysof determining RIQ may also be used such as, but not limited to, asimple Strehl ratio, point spread function, modulation transferfunction, compound modulation transfer function, phase transferfunction, optical transfer function, Strehl ratio in spatial domain,Strehl ratio in Fourier domain, or combinations thereof.

Visual acuity, as used herein, may sometimes be used as a measure of anaspect of visual performance. Visual acuity measurement evaluates thelimit when a visual target, such as a letter, or a letter “E”(illiterate′ E) or a letter “C” (Landolt C), or some other target, mayno longer be resolved, identified or correctly reported by the patientwho is undertaking the visual acuity measurement. The limit is relatedto, among other factors, the spatial frequency or spatial frequencies(how finely spaced the visual target details are) of the visual targetand the contrast of the visual target. The limit of visual acuity may bereached when the contrast of the image of the visual target, created bythe optics of an eye with or without additional optical devices, is toolow to be discerned by the visual system (including the retina, visualpathway and visual cortex).

The model eye used to evaluate the performance of certain exemplaryembodiments is Escudero-Navarro model eye with modifications to thelenticular surfaces to make it substantially aberration-free. However,the present disclosure is not limited to particular model eyes. Othermodel eyes may be used to evaluate the performance of embodimentsdisclosed herein. Some examples of such model eyes are:

a) A single refractive surface reduced model eye encompassing ananterior corneal surface and a retinal surface, wherein an intra-ocularfluid with a certain refractive index separates the above two surfaces;b) A reduced model eye with two refractive surfaces, which may be formedby addition of a posterior corneal surface to the model eye described in(a);c) A reduced model eye with three refractive surfaces, which may beformed by addition of two lenticular surfaces are added to the model eye(a) and the refractive index between the two lenticular surfaces beingsubstantially greater than the refractive index of the intra-ocularfluid;d) A model eye with four refractive surfaces, for example, Lotmar'smodel eye, Liou-Brennan's model eye, or Gullstrand's model eye;e) One of the model eyes discussed from (a) to (d), wherein one of thesurfaces disclosed may be substantially spherical;f) One of the model eyes discussed from (a) to (d), wherein one of thesurfaces may be substantially non-spherical;g) One of the model eyes discussed from (a) to (d), wherein one of thesurfaces may be substantially aspherical;h) One of the model eyes discussed from (a) to (d), wherein one of thesurfaces may be substantially decentred or tilted;(i) A modified model eye (d), wherein the refractive index in betweenthe lenticular surfaces may be considered to have gradient-refractiveindex; and(j) Personalised model eyes based upon the characteristic featuresmeasured of a particular human eye or a selected group of human eyes.

The performance of some exemplary embodiments may be evaluated withoutray-tracing through the combination of optical device, lens and theselected model eye, but instead with use of Fourier optics wherein thewavefront defined at the posterior surface of the lens is propagated tothe retinal space by adapting a two-dimensional Fourier transformation.

Section 1: Retinal Image Quality (RIQ)

With use of a wavefront aberrometer, such as a Hartmann-Shackinstrument, the optical characteristics of a candidate eye with orwithout refractive correction, model eye with or without refractivecorrection can be measured so as to identify a measure of retinal imagequality (RIQ). In some examples, the model eye used may be a physicalmodel that is anatomically, optically equivalent to an average humaneye. In certain examples, the RIQ can be calculated via opticalcalculation methods like ray-tracing and/or Fourier optics. Severalmeasures of RIQ are described herein.

(A) Strehl Ratio

Once the wavefront aberration of the candidate eye is availed, the imagequality at the retina of the eye can be determined by computing thesimple Strehl ratio, as described in the Equation 1. In certainapplications, the image quality at the retina of the eye may becharacterised by calculating a simple Strehl ratio as illustrated inEquation 1. The Strehl ratio can be computed in both spatial domain(i.e. using Point spread function as shown below in the equation 1(a)))and in Fourier domain (i.e. using Optical transfer function as shownbelow in equation 1(b)). The Strehl ratio measure is bound between 0 and1, where 1 is associated with best achievable image quality. In certainembodiments, the image quality produced by a lens and/or device at itsfocal distance may be calculated without the use of model eyes. Forexample, equations 1(a) and 1(b) may also be used without a model eye.

$\begin{matrix}{{{{Strehl}’}s{\mspace{11mu} \;}{ratio}{\mspace{11mu} \;}{in}\mspace{14mu} {spatial}\mspace{14mu} {domain}} = \frac{\int{\int_{- \infty}^{+ \infty}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}}{\int{\int_{- \infty}^{+ \infty}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}}} & {{Equation}\mspace{14mu} 1(a)} \\{{{{Strehl}’}s{\mspace{11mu} \;}{ratio}{\mspace{11mu} \;}{in}\mspace{14mu} {frequency}\mspace{14mu} {domain}} = \frac{\int{\int_{- \infty}^{+ \infty}( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} )}}{\int{\int_{- \infty}^{+ \infty}( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} )}}} & {{Equation}\mspace{14mu} 1(b)}\end{matrix}$

(B) Monochromatic RIQ

U.S. Pat. No. 7,077,522 B2 describes a vision metric called thesharpness metric. This metric can be computed by convolving a pointspread function with a neural quality function. Further, U.S. Pat. No.7,357,509 describes several other metrics to gauge optical performanceof the human eye. One such RIQ measure is the visual Strehl Ratio, whichis calculated in the frequency domain. In certain applications, the RIQmeasure is characterised by visual Strehl Ratio which is calculated inthe frequency domain. The visual Strehl Ratio in the frequency domain isdescribed by Equation 2 and is bound between 0 and 1, where 1 isassociated with best achievable image quality at the retina. This metricaddresses monochromatic aberrations.

$\begin{matrix}{{{monochromatic}\mspace{14mu} {RIQ}\mspace{14mu} {in}{\mspace{11mu} \;}{frequency}\mspace{14mu} {domain}} = \frac{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{{{CSF}( {f_{x},f_{y}} )}*}}} \\{{real}( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} )}\end{matrix}}{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{{{CSF}( {F_{x},f_{y}} )}*}}} \\( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} )\end{matrix}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

The RIQ measure of monochromatic visual Strehl Ratio shows highcorrelation with objective and subjective visual acuity. This measuremay be used to describe RIQ in certain disclosed embodiments. However,other measures described herein and alternatives thereto may be used inthe design of optical devices, lenses and/or methods.

(C) Polychromatic RIQ

The visual Strehl Ratio defined by Williams, discussed above, addressesmonochromatic light. To accommodate for polychromatic light, a metriccalled the polychromatic retinal image quality (polychromatic RIQ) isdefined that includes chromatic aberrations weighed with spectralsensitivities for selected wavelengths. The polychromatic RIQ measure isdefined in Equation 3. In certain applications, the polychromatic RIQmeasure may be used to describe RIQ which is characterised by Equation3.

$\begin{matrix}{{{polychromatic}\mspace{14mu} {RIQ}} = \frac{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{{{CSF}( {f_{x},f_{y}} )}*{\sum\limits_{\lambda \min}^{\lambda \max}( {{S(\lambda)}*} }}}} \\ ( {{real}( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} )} ) )\end{matrix}}{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{{{CSF}( {F_{x},f_{y}} )}*{\sum\limits_{\lambda \min}^{\lambda \max}( {{S(\lambda)}*} }}}} \\ ( ( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} ) ) )\end{matrix}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

(D) Monochromatic Global RIQ

The visual Strehl Ratio or monochromatic RIQ discussed herein and insub-section B primarily addresses on-axis vision. As used herein, unlessthe context clearly requires otherwise, ‘on-axis’ is a reference to oneor more of the optical, visual or papillary axis. To accommodate forwide angle view (i.e. peripheral visual field), a metric called theglobal retinal image quality (GRIQ) is defined that includes range ofvisual field eccentricities. A monochromatic GRIQ measure is defined inEquation 4. In certain applications, the monochromatic GRIQ measure ischaracterised by Equation 4.

$\begin{matrix}{{{monochromatic}\mspace{14mu} {Global}\mspace{14mu} {RIQ}\mspace{14mu} {in}\mspace{14mu} {frequency}\mspace{14mu} {domain}} = \frac{\begin{matrix}{\int_{\alpha \min}^{\alpha \max}{\int_{\phi \min}^{\phi \max}\{ {\int{\int_{- \infty}^{+ \infty}{{{CSF}( {f_{x},f_{y}} )}*}}} }} \\{ {{real}( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} )} \} d\; \phi \; d\; \lambda}\end{matrix}}{\begin{matrix}{\int_{\alpha \min}^{\alpha \max}{\int_{\phi \min}^{\phi \max}\{ {\int{\int_{- \infty}^{+ \infty}{{{CSF}( {f_{x},f_{y}} )}*}}} }} \\{ ( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} ) \} d\; \phi \; d\; \lambda}\end{matrix}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

(E) Polychromatic Global RIQ

One other form of RIQ metric that accommodates for polychromatic lightand wide angle view (i.e. peripheral visual field), a metric is calledthe polychromatic global retinal image quality (GRIQ) is defined thatincludes chromatic aberrations weighed with spectral sensitivities forselected wavelengths and range of visual field eccentricities. Apolychromatic GRIQ measure is defined in Equation 5. In certainapplications, the polychromatic GRIQ measure is characterised byEquation 5.

                                                                               Equation  5${{polychromatic}\mspace{14mu} {Global}\mspace{14mu} R\; I\; Q} = \frac{ {\int_{\alpha \; \min}^{\alpha \; \max}{\int_{\phi \mspace{11mu} \min}^{\phi \; \max}\{ {\int{\int_{- \infty}^{+ \infty}{{{CSF}( {f_{x},f_{y}} )}*{\sum\limits_{\lambda \; \min}^{\lambda \; \max}( {{S(\lambda)}*( {{real}( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} )} )} )}}}} }} \} d\; \phi \; d\; \lambda}{\int_{\alpha \; \min}^{\alpha \; \max}{\int_{\phi \mspace{11mu} \min}^{\phi \; \max}{\{ {\int{\int_{- \infty}^{+ \infty}{{{CSF}( {f_{x},f_{y}} )}*{\sum\limits_{\lambda \; \min}^{\lambda \; \max}( {{S(\lambda)}*( ( {{FT}( {{{FT}\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )} ) )} )}}}} \} d\; \phi \; d\; \lambda}}}$

In Equations 1 to 5:

-   -   f specifies the tested spatial frequency, this can be in the        range of F_(min) to F_(max) (denoting the boundary limits on the        spatial frequency content), for example F_(min)=0 cycles/degree;        F_(max)=30 cycles/degree; f_(x) and f_(y) specifies the tested        spatial frequency in x and y directions;    -   CSF (f_(x), f_(y)) denotes a contrast sensitivity function,        which in a symmetric form can be defined as CSF        (F)=2.6(0.0192+0.114*f)*exp^(−(0.114*f)̂1.1);    -   FT denotes, in one form of the equation, a 2D Fourier transform,        for example, a 2D fast Fourier transform;    -   A(ρ, θ) and W(ρ, θ) denotes pupil amplitude function across the        pupil diameter and wavefront of the test case, respectively;    -   Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;    -   ρ and θ are normalised polar coordinates, where ρ represents the        radial coordinate and θ represents the angular coordinate or the        azimuth;    -   λ denotes wavelength;    -   α denotes field angle;    -   φ denotes the meridian angle;    -   S (λ) denotes spectral sensitivity.

The wavefront, for example, can be written as a function set of standardZernike polynomials up to a desired order, as described below,

${W( {\rho,\theta} )} = {\sum\limits_{i = 1}^{k}{a_{i}{Z_{i}( {\rho,\theta} )}}}$

Where, a₁ denotes the i^(th) coefficient of Zernike polynomial

-   -   Z_(i)(ρ, θ), denotes the i^(th) Zernike polynomial term    -   ‘k’, represents the highest term of the expansion

These polynomials can be represented in the Optical Society of Americaformat or Malacara format or other available Zernike polynomialexpansion formats. Apart from the Zernike method of constructing thewavefront and/or wavefront phase, other non-Zernike methods of wavefrontconstruction may also be adopted, i.e., Fourier expansion, Taylorexpansion, Bessel functions, even polynomials, odd polynomials, sum ofsine, sum of cosine, super conics, Q-type aspheres, B-splines, waveletsor combinations thereof. Spectral sensitivity functions may be selectedfor use in equation 5, for example, from population average; specificlighting conditions such as photopic, mesopic or scotopic conditions;sub-population averages such as a specific age group; a specificindividual or combinations thereof.

(F) Global RIQ Metric Integrated Myopic Impetus Exposure Time

The factors discussed herein with regard to RIQ variants include one ormore of the following: wavefront aberration, chromaticity and spectralsensitivity, Stiles-Crawford effect of the first kind, and opticaland/or visual performance in the peripheral retina. Another factor thatmay be included is the amount of time spent at various accommodativestates on an average day (the daily amount of near work), also known asthe myopic impetus exposure time, T (A). This provides the followingGRIQ variant:

∫_(Amin) ^(Amax) T(A)*GRIQ(dA)   Equation 6

(G) Other Possible RIQ Measures

As discussed herein, other measures of RIQ may also be used in thedesign of devices, lenses and/or methods. One example of an alternativeRIQ measure is simple modulation transfer function (MTF). Referring toEquation 2, a polychromatic MTF is formed by computing the modulus ofreal part of the optical transfer function and in addition excluding thestep of convolution with the CSF function. A monochromatic MTF is formedif S (λ) is also removed from Equation 2.

Other measures of RIQ used in the designs of devices, lenses and/ormethods may include multifocal benefit ratio. Referring to Equation 2, amultifocal benefit ratio metric may be computed by dividing the RIQmetric for the design with the RIQ metric obtained for a single visionlens. This multifocal benefit ratio may further be computed at variousdioptric vergences, thereby providing through-focus multifocal benefitratio.

No of phase reversals may be included as one other measure of RIQ usedin the designs of devices, lenses and/or methods. The number of phasereversals metric may be obtained from the phase transfer function. Thephase transfer function is obtained as the inverse tangent angle ofimaginary part of the optical transfer function divided by the real partof the optical transfer function. Non-linear optimisation routines maybe deployed to find designs solutions that reduce the number of phasereversals across a range of dioptric vergence.

Another measure of RIQ that may be used in the designs of devices,lenses and/or methods is to include a Phase transfer functioninformation in the monochromatic RIQ or the visual Strehl ratiocalculations. For example, one method of including phase transferinformation in the visual Strehl ratio calculations is to convolve thereal part of the optical transfer function in the Equation 2 with cosineof the phase transfer function as described in the equation 7.

                                      Equation  7${{monochromatic}\mspace{14mu} R\; I\; Q\mspace{14mu} {in}\mspace{14mu} {frequency}\mspace{14mu} {domain}\mspace{14mu} {with}\mspace{14mu} P\; T\; F} = \frac{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{C\; S\; {F( {f_{x},f_{y}} )}*{\cos ( {P\; T\; {F( {f_{x},f_{y}} )}} )}*}}} \\{{real}( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} )}\end{matrix}}{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{C\; S\; {F( {f_{x},f_{y}} )}*{\cos ( {P\; T\; {F( {f_{x},f_{y}} )}} )}*}}} \\( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} )\end{matrix}}$

Another measure of RIQ that may be used in the designs of devices,lenses and/or methods is to include a weighted contrast sensitivityfunction and weighted phase transfer function information in themonochromatic RIQ calculations.

                                                                     Equation  8${{monochromatic}\mspace{14mu} R\; I\; Q\mspace{14mu} {in}\mspace{14mu} {frequency}\mspace{14mu} {domain}\mspace{14mu} {with}\mspace{14mu} {wieghted}\mspace{14mu} P\; T\; F\mspace{14mu} {and}\mspace{14mu} C\; S\; F} = {\quad\frac{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{( {a*C\; S\; {F( {f_{x},f_{y}} )}} )*( {b*{\cos ( {P\; T\; {F( {f_{x},f_{y}} )}} )}} )*}}} \\{{real}( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} )}\end{matrix}}{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{( {a*C\; S\; {F( {f_{x},f_{y}} )}} )*( {b*{\cos ( {P\; T\; {F( {f_{x},f_{y}} )}} )}} )*}}} \\( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} )\end{matrix}}}$

-   -   where a and b are weights applied to CSF (f_(x), fy) and PTF        (f_(x), fy) respectively.

Another measure of RIQ that may be used in the designs of devices,lenses and/or methods is to include individualised contrast sensitivityfunction for a particular human eye.

                                                                    Equation  9${{monochromatic}\mspace{14mu} R\; I\; Q\mspace{14mu} {in}\mspace{14mu} {frequency}\mspace{14mu} {domain}\mspace{14mu} {for}\mspace{14mu} a\mspace{14mu} {particular}\mspace{14mu} {human}\mspace{14mu} {eye}} = {\quad\frac{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{( {{Indv\_ CSF}( {f_{x},f_{y}} )} )*{\cos ( {P\; T\; {F( {f_{x},f_{y}} )}} )}*}}} \\{{real}( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} )}\end{matrix}}{\begin{matrix}{\int{\int_{- \infty}^{+ \infty}{( {{Indv\_ CSF}( {f_{x},f_{y}} )} )*{\cos ( {P\; T\; {F( {f_{x},f_{y}} )}} )}*}}} \\( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} )\end{matrix}}}$

Where Indv_CSF is contrast sensitivity function of a particular humaneye for which the optical device, lens and/or method is being applied.

Other measures of RIQ that may be used in the designs of devices, lensesand/or methods may include two dimensional correlation analysis inspatial domain. Two dimensional correlation analysis in spatial domainis performed by obtaining the correlation coefficient when the pointspread function of the optimised design is correlated with the pointspread function of the diffraction limited system. Such correlationcoefficients may be obtained for numerous configurations spanningvarious pupil diameters and/or distance ranges. The correlationcoefficient obtained may range from −1 to 1, where values close to −1indicates high negative correlation, values close to 0 indicate poorcorrelation and values close to 1 indicate high positive correlation.For the purpose of the correlation analysis, simulated images may beused for correlation analysis that are obtained by convolving pointspread function with the objects in image space.

Other measures of RIQ that may be used in the designs of devices, lensesand/or methods may include two dimensional correlation analysis infrequency domain. Two dimensional correlation analysis in frequencydomain is performed by obtaining the correlation coefficient when theoptical transfer function of the optimised design is correlated with theoptical transfer function of the diffraction limited system. Suchcorrelation coefficients may be obtained for numerous configurationsspanning various pupil diameters and/or distance ranges. The correlationcoefficient obtained may range from −1 to 1, where values close to −1indicates high negative correlation, values close to 0 indicate poorcorrelation and values close to 1 indicate high positive correlation.For the purpose of the correlation analysis, one of the following inputvariables may be selected: real part of optical transfer function,imaginary part of optical transfer function, modulation transferfunction and phase transfer function.

Section 2: Through Focus RIQ

RIQ may also be considered anterior and/or posterior to the retina. TheRIQ anterior and/or posterior to the retina is called ‘through focusRIQ’ herein and abbreviated as TFRIQ herein. Similarly, RIQ at and/oraround the retina may also be considered over a range of focal lengths(i.e., when the eye accommodates, which causes changes in refractivecharacteristics of the eye in addition to the focal length to change).Certain embodiments may consider not only RIQ at the retina, but alsothe change in through focus RIQ. This is in contrast to an approach thatmay, for example, consider only the RIQ at the retina and/or an integralor summation of RIQ measures at or around the retina. For example,certain embodiments of the lenses, devices and/or methods disclosedherein effect, or are designed to effect for an eye with particularrefractive characteristics, a change in or control over the extent orrate of change in RIQ in the directions anterior to the retina (i.e.,the direction from the retina towards the cornea) and/or posterior tothe retina. Certain embodiments may also effect, or are designed toeffect, a change in or control over the variation in RIQ with focaldistance. For example several candidate lens designs may be identifiedthrough effecting a change in the RIQ in the direction posterior to theretina and then a single design or subset of designs may be identifiedtaking account of variation in RIQ with change in focal length. Incertain embodiments, the process described above is reversed. Inparticular, a set of designs is selected based on changes in RIQ at theretina with focal distance. Selection within the set is then made withreference to the TFRIQ. In certain embodiments, a single evaluationprocess is conducted that combines consideration of TFRIQ and changes ofRIQ at the retina with the focal distance. For example, an averagemeasure of RIQ with changes in focal distance may be used to identify adesign. The average measure may give more weight to particular focaldistances (e.g. distance vision, intermediate vision and near vision andtherefore may be weighted differently).

For example, an average measure of RIQ with changes in focal distancemay be used to identify a design that may be used with certain devices,lenses and/or methods disclosed herein. For example, a measure of RIQaveraged over a range of focal distances. The average measure may be aweighted average measure that may give more weight or emphasis toparticular focal distances (e.g. distance vision, intermediate visionand near vision and therefore may be weighted differently).

RIQ may also be considered anterior and/or posterior to the retina. TheRIQ anterior and/or posterior to the retina is called ‘through focusRIQ’ herein and abbreviated as TFRIQ. Similarly, RIQ at and/or aroundthe retina may also be considered over a range of focal lengths. Forexample, when the eye accommodates, which causes changes in refractivecharacteristics of the eye its focal length also changes. Certainembodiments may consider not only RIQ at the retina, but also the changein through focus RIQ. This is in contrast to an approach that may, forexample, consider only the RIQ at the retina and/or an integral orsummation of RIQ measures at or around the retina. For example, certainembodiments of the lenses, devices and/or methods disclosed hereineffect, or are designed to effect for, an eye with particular refractivecharacteristics, a change in or control over the extent or rate ofchange in RIQ in the directions anterior to the retina (i.e., thedirection from the retina towards the cornea) and/or posterior to theretina. Certain embodiments may also effect, or are designed to effect,a change in or control over the variation in RIQ with focal distance.For example, several candidate lens designs may be identified througheffecting a change in the RIQ in the direction posterior to the retinaand then a single design or subset of designs may be identified takingaccount of variation in RIQ with change in focal distance. In someembodiments, the process described above is reversed. In particular, aset of designs is selected based on changes in RIQ at the retina withfocal distance. Selection within the set is then made with reference tothe TFRIQ. In some embodiments, a single evaluation process is conductedthat combines consideration of TFRIQ and changes of RIQ at the retinawith the focal distance. For example, an average measure of RIQ withchanges in focal distance may be used to identify a design that may beused with certain devices, lenses and/or methods disclosed herein. Theaverage measure may give more weight to particular focal distances(e.g., distance vision, intermediate vision and near vision andtherefore may be weighted differently). In certain embodiments, throughfocus and/or changes of RIQ at the retina with focal distance areconsidered for one or more of the following: i) on-axis, ii) integratedaround on-axis, for example in an area corresponding to or approximatinga pupil size, with or without consideration of the Stiles-Crawfordeffect, iii) off-axis (where off-axis means a location, set of locationsand/or integral of locations on the retina outside the fovea, which maybe where light at field angles more than about 10 degrees is focussed),and iv) one or more combinations of i) to iii). In certain applications,the field angles are about 15 or more, 20 or more, 25 or more or 30 ormore degrees.

While the description herein refers to quantitative measures of RIQ,qualitative measures may also be used to assist the design process of anaberration profile in addition to the quantitative measures. Forexample, the visual Strehl Ratio at a particular through focus locationis computed or determined based on the point spread function. As can beseen from the example images referred to in the following section, thepoint spread function can be visually evaluated. This provides for amethod of qualitatively evaluating through focus.

In some embodiments, an image quality produced by a lens and/or deviceat its focal distance is computed without the use of a model eye. Theimage quality produced by a lens and/or device may be calculatedanterior and/or posterior to the focal distance of the lens and/ordevice. The image quality anterior and/or posterior to the focaldistance may be referred to as through focus image quality. Thethrough-focus range has a negative and a positive power end relative tothe focal distance.

Section 3: Aberrations Affecting Image Quality at the Retina and TFRIQ

The influence of lower order aberrations on RIQ and TFRIQ is known inthe art. The use of corrective lower order aberrations represents atraditional method of refractive error correction for an eye.Accordingly, the identification of an aberration profile consisting oflower order aberrations to correct for defocus and astigmatism will notbe described herein in detail.

The influence of higher order aberrations (HOA) on image quality isdemonstrated in FIG. 3 from the through-focus two-dimensional pointspread functions (300). In FIG. 3 the rows show the point spreadfunctions for a selection of aberrations and the horizontal axis showsthe extent of defocus for the relevant aberration, in Dioptres.

Exemplary HOA on image quality are illustrated in FIG. 3, according tocertain embodiments. This is illustrated by the through-focustwo-dimensional point spread functions 300 illustrated in FIG. 3. InFIG. 3, the rows show the point spread functions for a selection ofaberrations and the horizontal axis shows the extent of defocus for thecertain relevant aberration, in Dioptres.

The point spread functions without higher order aberrations 302 (in theillustrated example images at the retina in an eye with myopia orhyperopia alone), with vertical coma 306 alone, and with horizontaltrefoil 308 alone, remain symmetrical with positive and negativedefocus. With positive and negative primary spherical aberrations,either alone 304 or in combination 310 with coma and/or trefoil, thethrough-focus in the point spread function is asymmetrical for positiveand negative defocus. With certain HOA positive and negative defocus hasunequal effects on the image quality. It can be seen that these unequaleffects are more pronounced for spherical aberrations. The HOA thatexhibit asymmetrical effects on RIQ, visual acuity and/or contrastsensitivity have application certain of the lenses, devices and/ormethods disclosed herein.

The interactions occurring between HOA and defocus influence the TFRIQ.Some HOA interact favourably with defocus to improve RIQ, while othersinteract unfavourably to cause RIQ degradation. The most commonlymeasured higher order ocular aberrations include spherical aberration,coma and trefoil. Apart from these, the HOA profiles obtained with somemultifocal optical designs precipitate considerable magnitudes ofwavefront aberrations, often expressed up to the 10th order in Zernikepolynomial representation.

In general terms, in the Zernike pyramid, the terms closer to the centreare often more influential, or useful, when gauged in terms of theresultant optical effects than those at the edge/corner. This may bebecause the terms farther away from the centre have a relatively largeplanar area on the wavefront compared to those whose angular frequencyis closer to zero. In certain applications, Zernike terms that have thehighest potential, or substantially greater potential, to interact withdefocus are, for example, the terms with even radial order having zeroangular frequency component, i.e., the fourth, sixth, eighth, and tenthorder Zernike coefficients, representing primary, secondary, tertiaryand quaternary, spherical aberrations. Other Zernike coefficientsrepresenting other order of spherical aberration may also be used.

The foregoing description of aberrations identifies some of theaberrations that affect retinal RIQ and through focus RIQ. Thedescription is not, nor is it intended to be, an exhaustive descriptionof the various aberrations that affect retinal RIQ and through focusRIQ. In various embodiments, additional aberrations that affect theretinal RIQ and/or through focus RIQ may be considered, the relevantaberrations being identified having regard to the current refractivestate of the ocular system (meaning the eye together with lenses oroptical devices that affect the wavefront received by the retina) and atarget retinal RIQ/through focus RIQ.

Section 4: Optimising RIQ

When designing and/or selecting a required change in refractive state ofan eye, a measure of RIQ and through focus RIQ is typically performedfor certain disclosed embodiments. In particular, finding a magnitudeand sign of defocus that interacts with one or more of the relevantaberrations and produce an acceptable RIQ and through focus RIQ istypically performed. The search is performed for the best or at least anacceptable combination of RIQ and through focus RIQ. In certainembodiments, the selected combination is determined by evaluating theRIQ and the through focus RIQ and selecting the combination that issuitable, substantially optimised, or optimised for the application. Incertain embodiments described herein, a merit function S=1/RIQ is usedfor this purpose. In certain embodiments, the approximation of a meritfunction S=1/RIQ may be used for this purpose.

Identifying aberration coefficients that optimise, or substantiallyoptimise, RIQ at the retina may be achieved, in certain embodiments; byfinding a minimum, or substantially minimum, value of the function S.Considering the RIQ optimisation routine over a range of dioptricdistances (through-focus) adds complexity to the optimisation process.Various methods can be used to address this complexity.

One example is to use a non-linear, unconstrained optimization routine,over the chosen group of Zernike SA coefficients as variables, accordingto certain embodiments. A random element, either automatic and/orthrough human intervention may be incorporated to shift to differentlocations so as to find alternative local minima of the function S. Thecriteria by which the optimisation routine evaluates performance may bea combination of retinal RIQ and keeping the through focus RIQ withinpredefined bounds of the retinal RIQ. The bounds may be defined invarious ways, for example as a range about the value for retinal RIQ.The range may be fixed (e.g. plus or minus 0.15 for visual Strehl ratioor similar measure), or may vary (e.g. be within a defined rate ofchange with increasing distance from the retina). In certainembodiments, the range may be fixed to one or more of the followingranges: plus or minus 0.05, or plus or minus 0.1 or plus or minus 0.15.These ranges may be used with one or more of the following: a simpleStrehl ratio, point spread function, modulation transfer function, phasetransfer function, optical transfer function, Strehl ratio in Fourierdomain, or combinations thereof.

As explained in more detail herein, the goal function for TFRIQ maychange depending on whether the objective of the merit function is toprovide a TFRIQ with a slope that provides stimulus either to inhibit orto encourage eye growth of the candidate eye, under an optical feedbackexplanation of emmetropisation, at least in certain embodiments. Incertain other applications, for example correction to amelioratepresbyopia, the objective of the merit function is to provide a TFRIQwith an acceptable low slope in magnitude or a slope that substantiallyequal to zero. In certain other presbyopic embodiments, a slope withacceptably low in magnitude for TFRIQ may be considered from one or moreof the following: a) slope of TFRIQ about zero, b) slope of TFRIQ equalto zero, c) slope of TFRIQ greater than zero and less than 0.25 perdioptre, d) slope of TFRIQ greater than −0.25 and less than zero perdioptre, e) slope of TFRIQ greater than zero and less than 0.5 perdioptre or f) slope of TFRIQ greater than −0.5 and less than zero perdioptre.

Another approach is to limit the number of possible combinations ofaberration profiles. One way of limiting the possible aberration valuesis to specify that the Zernike coefficients can only have valuescorresponding to increments of 0.05 μm focus, or another incrementinterval. In certain embodiments, the Zernike coefficients may havevalues corresponding to increments of about 0.01 μm, about 0.02 μm,about 0.03 μm, about 0.04 μm or about 0.05 μm. In certain embodiments,the Zernike coefficients may have values corresponding to increments of0.01 μm, 0.02 μm, 0.03 μm, 0.04 μm or 0.05 μm. In certain embodiments,the Zernike coefficients may have values corresponding to fromincrements selected within one or more following ranges: 0.005 μm to0.01 μm, 0.01 μm to 0.02 μm, 0.02 μm to 0.03 μm, 0.03 μm to 0.04 μm,0.04 μm to 0.05 μm, or 0.005 μm to 0.05 μm. The interval can be selectedhaving regard to the available computational resources. By limiting thenumber of allowable coefficient values it is possible to simulate theperformance of a substantial portion of the aberration profiles formedby the combinations of Zernike coefficients, following which those withthe best or acceptable on-axis RIQ and through focus RIQ can beidentified. The results of this process may be used to constrain morefine-tuned analysis, for example by returning to an optimisation routinewith coefficient values within a small range around an identifiedcandidate combination of higher order aberrations.

Section 5: Controlling Stimulus for Emmetropisation by Optical Feedback

A person may be identified as being at risk of developing myopia basedon, for example, one or more of the following indicators, includingwhether their parents experienced myopia and/or myopia, their ethnicity,lifestyle factors, environmental factors, amount of near work, etc.Other indications or combinations of indicators may also be used,according to certain embodiments. For example, a person may beidentified as being at risk of developing myopia if their eye and/oreyes have a RIQ at the retina that improves in the direction of eyegrowth. The RIQ can be obtained either with or without refractivecorrection that is currently in use (for example: with or without acurrent prescription of spectacle or contact lens). In certainembodiments, the use of improving RIQ in the direction of eye growth maybe used alone or in conjunction with one or more other indicators, forexample the other indicators listed herein.

From one perspective, the emmetropisation process can be explained underan optical feedback mechanism that is based on RIQ at the retina and/orthe slope of TFRIQ in the anterior-posterior direction to the retina.According to this perspective on emmetropisation, the candidate eye isstimulated to grow to the position where the merit function S of theoptimisation routine is minimised or substantially minimised. Under thisexplanation of emmetropisation process, at least for human eyes, if thelocation of a local, or the global minimum of the merit function S, thenthe eye may be stimulated to grow longer, in certain embodiments. In yetanother application, the substantial minimum of the merit functionoptimisation routine may be a local minimum or global minimum. In otherapplications, if the location of a local or the global minimum of themerit function S is posterior to the retina or if through focus RIQimproves posterior to the retina, then the eye may be stimulated to growlonger. For example, if the location of a local or the global minimum ofthe merit function S is located on the retina or anterior to the retina,then the eye may remain at the same length.

The following description herein describes how combinations of selectedHOA can affect a change in through focus RIQ. These aberrations canreadily be incorporated into a lens, optical device and/or used in amethod of changing the aberration profile of the wavefront of theincoming light received by the retina.

In certain embodiments, characterizations of these aberrations canreadily be incorporated into a lens, optical device and/or used in amethod of changing the aberration profile of the wavefront of theincoming light received by the retina. This provides a mechanism bywhich certain embodiments may change the refractive state of a candidateeye. In certain embodiments, the lens, optical device and/or method willat least include the aberration characteristics of the embodiments toalter the refractive state of a candidate eye.

As described in more detail herein, achieving a target TFRIQ isconsidered together with achieving or obtaining substantially closer toa target on-axis RIQ at the retina for a particular focal length, whichis typically distance vision, in certain embodiments, In certainapplications, one or more of the following are referred as distancevision is objects greater than 6 metres. In other applications, a targetTFRIQ may be considered for another focal length alternative to distancevision, for example intermediate vision or near vision. In someapplications, intermediate vision may be defined as the range from about0.5 to 6 metres. In some applications, near vision may be defined as therange from 0.3 to 0.5 metres.

As described in more detail herein, achieving a target TFRIQ isconsidered together with achieving or obtaining substantially closer toa target on-axis RIQ at the retina for a particular focal distance,which is typically distance vision, One or more of the following may bereferred to as distance vision objects greater than 6 metres. In someembodiments, a target TFRIQ may be considered for another focal distancealternative to distance vision, for example intermediate vision or nearvision. In some embodiments, intermediate vision may be defined as therange from about 0.5 to 6 metres. In some applications, near vision maybe defined as the range from 0.3 to 0.5 metres.

For the examples described herein the RIQ was evaluated, orcharacterised by, using the visual Strehl Ratio shown in Equation 2.

(A) Primary Spherical Aberration, Coma and Trefoil

The interactions between primary spherical aberration, coma and trefoiland their affect on eye growth can be described, or characterised by,using a wavefront phase function defined using defocus, primaryspherical aberration (PSA), coma and trefoil terms of a standard Zernikeexpansion. Other ways are also possible.

The pupil size was fixed at 4 mm and the calculations were performed at589 nm wavelength. For the purposes of evaluating affects of aberrationprofiles on ocular growth, it was assumed that a location of a minimumof the above described function S posterior to the retina provides astimulus to grow to that location and that there will not be stimulusfor eye growth if the minimum of the function S is on or in front of theretina. In other words, it is assumed that the image formed on theretina provides a stimulus to grow to minimise the function S. The rangeof values of PSA, horizontal and vertical coma, and horizontal andvertical trefoil that were used in the simulations are:

PSA=(−0.30, −0.15, 0.00, 0.15, 0.30) μm

Horizontal Coma=(−0.30, −0.15, 0.00, 0.15, 0.30) μm

Vertical Coma=(−0.30, −0.15, 0.00, 0.15, 0.30) μm

Horizontal Trefoil=(−0.30, −0.15, 0.00, 0.15, 0.30) μm and

Vertical Trefoil=(−0.30, −0.15, 0.00, 0.15, 0.30) μm.

With a total of 3125 combinations tested, overall it was observed thatspherical aberration primarily governed the direction of improving RIQ.

FIGS. 4 to 7 illustrate the stimulus for eye growth resulting from TFRIQfor a selection of the combinations, in particular the combined effectsof PSA together with horizontal and vertical coma, and together withhorizontal and vertical trefoil, in accordance with certain embodiments.FIGS. 4 to 7 are on a continuous scale and white (0) indicates noprogression and grey-to-black transition indicates the amount ofprogression in Dioptres.

FIG. 4 shows a graph 400 of the interaction of primary sphericalaberration and horizontal coma. The grey plot indicates the amount ofprogression of myopia that is stimulated by the combination of these twoaberrations, where white 402 indicates no stimulus for progression andshades towards black 404 indicate stimulus for progression of myopia (inthis case up to −0.8 D) as a result of PSA combined with horizontalcoma. FIG. 5 shows a graph 500 of myopia progression as a function ofthe interaction of primary spherical aberration and vertical coma. Likein FIG. 4, white areas 502 indicate no stimulus for progression and darkareas 504 indicate stimulus for progression. FIG. 6 shows a graph 600 ofthe interaction of primary spherical aberration and horizontal trefoil.FIG. 7 shows a graph 700 of myopia progression as a function of theinteraction of primary spherical aberration and vertical trefoil. Forthe combinations shown in FIGS. 4 to 7, about 52% of the combinationsprovide stimulus to encourage eye growth.

Stimulus for eye growth may accordingly be removed by controlling therefractive state of an eye to be within one or more of the white areasin FIGS. 4 to 7. This may be achieved, for example, by designing a lensor optical device that when applied modifies the refractivecharacteristics of the eye, to result in the retina of the eyeexperiencing a through focus RIQ that does not substantially improve, ordoes not improve, in the direction of eye growth (posterior to theretina) or which decreases in the direction of eye growth.

Although trefoil and coma in the range of −0.30 to 0.30 μm over a 4 mmpupil do not appear to have a significant impact on the direction ofgrowth (the maximum progression effect is only −0.1D), positive PSAseems to accelerate growth while negative PSA seems to inhibit growth.The PSA therefore appears to have the dominant effect. Accordingly, atleast for an eye with positive PSA and optionally one of coma andtrefoil, adding negative PSA may inhibit eye growth under the opticalfeedback explanation of emmetropisation. It follows that providingnegative PSA to an eye, or at least removing positive PSA may remove thestimulus for eye growth. The coma and trefoil in the eye may be leftunchanged or optionally partially or fully corrected (preferably withinthe range of −0.30 to 0.30 μm).

(B) Spherical Aberration and Astigmatism Interaction

To illustrate the interactions between primary spherical aberration andastigmatism, a wavefront phase function was defined using theseaberrations (including both horizontal/vertical and oblique components)and defocus. FIGS. 8 to 13 (unlike FIGS. 4 to 7) are on a binaryscale—where white (1) indicates test cases that cause stimulus forprogression (i.e. increase in ocular growth) and black (0) indicatescandidate combinations that result in no progression or very littleprogression (i.e., no ocular growth stimulus or a stop signal). Thescale has no units. FIGS. 8 to 13 illustrate certain disclosedembodiments.

FIG. 8 is an exemplary that shows a graph 800 indicating the magnitudeof myopia progression for PSA vs. a primary oblique astigmatic component(POA) vs. a primary horizontal/vertical astigmatic (PHV) component. Inthis example, the graph 800 indicates those combinations of PSA andastigmatism that may result in stimulus for myopia progression (white)and those combinations that will not result in stimulus for myopiaprogression (black). Neither POA nor PHV appear to have a significantimpact on the effects of PSA.

FIG. 9 is an exemplary shows a graph 900 indicating the magnitude ofmyopia progression for PSA vs. a secondary oblique astigmatic (SOA)component vs. a secondary horizontal/vertical astigmatic (SHV)component, according to certain embodiments. In this example, neitherSOA nor SHV appear to have a significant impact on the effects of PSA.

A stimulus for eye growth may accordingly be removed by controlling therefractive state of an eye to be within one or more of the white areasin FIGS. 8 and 9.

From FIGS. 8 and 9, is an exemplary, the primary and secondaryastigmatic components seem to have, or have, a small influence onenhancing or inhibiting eye growth, when combined with PSA. Accordingly,considering these aberrations, this indicates priority may be providedto PSA. In addition, it may be determined whether the eye has highlevels of POA, PHV, SOA and/or SHV. If this is the case, in thisexample, then correcting these aberrations (by reducing or substantiallyeliminating them) may also assist in removing stimulus for eye growth.

(C) Higher Order Spherical Aberrations

For unaided or single-vision spectacle corrected eyes a fourth orderZernike expansion may be used to describe, or characterise, thewavefront at the exit pupil. However, this may not necessarily the casewhen, for example, contact lenses are used for correction, especiallywith multifocal contact lenses (both aspheric and concentric),substantial amounts of fifth order and higher HOA may be used.Multifocal contact lenses may, for example, be described using up toabout the tenth or twentieth order of Zernike polynomials. In such casesthe magnitudes and signs of the higher order spherical aberrations startto play a significant role (in addition to PSA).

To illustrate the interactions between primary, secondary, tertiaryand/or quaternary spherical aberrations of a standard Zernike expansion,a wavefront phase was defined using these terms and defocus. Severalcombinations of HOA as predicted from modelled data with such multifocalcontact lenses were used. Selective sets of these HOA that demonstrateinteractions to produce peak RIQ were obtained via dedicated non-linearoptimization routines. The calculations were performed over a 4 mmpupil, and at 589 nm wavelength. It was observed that at least the firstthree modes of spherical aberration of the inherent eye played a role ingoverning the direction of stimulus for eye growth and in some caseshigher modes of spherical aberration also played a role. In certainapplications, these roles were significant.

The results described below relate to secondary spherical aberration(SSA), tertiary spherical aberration (TSA) and quaternary sphericalaberration (QSA), but spherical aberrations with higher orders may alsobe used in embodiments of the lenses, devices and/or methods describedherein.

For four types of spherical aberrations, a range from −0.30 to 0.30 μmwas used to investigate the effects of the combinations of HOA. Theseranges for these types of aberrations do not necessarily accord withnormative distributions of aberrations associated with eyes because theoccurrence of these higher order aberrations are not necessarilyassociated with the eyes but with the optical devices (such asmultifocal contact lenses) alone or in combination with the eyes.Furthermore, the range from −0.30 to 0.30 μm is merely used toillustrate the effects, but when determining combinations of HOA toprovide an aberration profile in a lens or optical device, or to beeffected by surgical procedures, larger or smaller ranges may be used.

FIGS. 10 to 12 are exemplary that show the stimulus for myopiaprogression as a function of PSA together with SSA, TSA and QSArespectively, according to certain embodiments. In this example, thisschema is a binary colour plot, where white (0) indicates wavefrontaberration combinations that provide stimulus for myopia progressionunder the feedback mechanism described herein and black (1) indicatescombinations that discourage myopia progression. From these graphs it isapparent that the higher orders of spherical aberrations have an impacton the stimulus for progression of myopia. In this example, about 82% ofthe combinations investigated suggest stimulus for eye growth.Interactions of the spherical aberration terms depend on theirindividual signs and then their individual magnitudes.

FIG. 10 is an exemplary that shows a graph 1000 indicating the presenceof stimulus for myopia progression as a function of combinations of PSAand SSA, according to certain embodiments. In FIG. 10, it can be seenthat when PSA in the range −0.30 μm to 0.20 μm is combined with negativeSSA ranging from 0.00 to −0.30 μm, there is little or no improvement ofRIQ in the direction of eye growth, thus no myopia progression ispredicted (i.e. in the area indicated 1004). However, when PSA rangingfrom 0.20 to 0.30 μm is considered with negative SSA of about −0.10 μm,it seems to aggravate the progression, as indicated in the area 1002.Overall, the sign of SSA seems to have a governing effect on the effectof the wavefront aberrations and the resultant retinal image quality. Inthis example, negative SSA of considerable magnitudes (i.e. greater than−0.20 μm) predicts a protective effect against myopia progression whencombined with either positive or negative PSA, when PSA and SSA are theonly two HOA involved in the wavefront aberration of the candidate eye.

FIG. 11 is an exemplary that shows a graph 1100 indicating the presenceof stimulus for myopia progression as a function of combinations of PSAand TSA, according to certain embodiments. When PSA and TSA have thesame sign and TSA is about ⅘th of PSA in magnitude, as indicated byrectangular box 1106, no or little myopia progression is predicted(black area). However, in this example, with other combinations of PSAand TSA, for example as indicated in areas 1102 and 1104, myopiaprogression can be expected.

FIG. 12 is an exemplary that shows a graph 1200 indicating the presenceof stimulus for myopia progression as a function of combinations of PSAand QSA, according to certain embodiments. In this example, when PSA andQSA have opposite signs and QSA is about ⅘th of PSA in magnitude, asindicated by the predominantly black area 1204, no myopia progression ispredicted. However, with other combinations of PSA and QSA, (for exampleas indicated in white areas 1202 and 1206) myopia progression can beexpected.

FIG. 13 is an exemplary that is a graph (1300) showing the presence ofstimulus for progression of myopia as a function of PSA, SSA and TSA,according to certain embodiments. This schema is a binary colour plot,where 1 (white) indicates wavefront aberration combinations that favourmyopia progression; while 0 (black) indicates combinations thatdiscourage myopia progression (i.e. do not provide stimulus for eyegrowth).

TABLE 1 Combination sets of higher order aberrations which discouragethe eye growth (i.e. potential treatment for myopia), according tocertain embodiments. Specific higher order aberration in addition to SNodefocus Magnitude and sign of the higher order aberration 1 PSA only−0.30 μm <= PSA < 0.125 μm 2 SSA only −0.30 μm <= SSA <= 0.075 μm 3 TSAonly −0.30 μm <= TSA <= 0.075 μm 4 QSA only −0.10 μm <= QSA <= 0.075 μm5 PSA & SSA −0.30 μm <= PSA <= 0.20 μm and −0.25 μm <= SSA <= 0.025 μm 6PSA & TSA −0.30 μm <= PSA <= 0.30 μm and TSA = (PSA/2)μm +/− 0.075 μm 7PSA & QSA −0.30 μm <= PSA <= 0.30 μm and QSA = (|PSA|/3) μm +/− 0.075 μm8 PSA, SSA, TSA −0.30 μm <= PSA < −0.05 μm & 0.05 μm < PSA < 0.30 μm;−0.30 μm <= SSA < 0.05 μm; −0.20 μm <= TSA < −0.025 μm & 0.025 μm < TSA< 0.20 μm; 9 PSA, SSA, TSA and QSA −0.30 μm <= PSA < −0.05 μm & 0.05 μm< PSA < 0.30 μm; −0.30 μm <= SSA < 0.05 μm; −0.20 μm <= TSA < −0.025 μm& 0.025 μm < TSA < 0.20 μm; −0.20 μm <= QSA < −0.025 μm & 0.025 μm < QSA< 0.20 μm;

The majority of the black filled circles 1304 are in the region governedby negative SSA, with a few exceptions. Further, combinations in whichPSA and TSA have the same sign coupled with negative SSA seem to providea protective effect against myopia progression. The combinations of PSA,SSA, TSA and QSA that have a protective effect against myopiaprogression under the optical feedback explanation of emmetropisation(which include the black areas shown in FIG. 13) can be summarised asshown in the Table 1.

The majority of the white circles 1302 are in the region governed bypositive SSA, with a few exceptions. Further, combinations in which thePSA and TSA have the same sign coupled with positive SSA may provide atreatment effect for hyperopia. The combinations of PSA, SSA, TSA andQSA that have a treatment effect against hyperopia under the opticalfeedback explanation of emmetropisation (including the white areas shownin FIG. 13) can be summarised as shown in the Table 2.

TABLE 2 Combination sets of higher order aberrations which encourage eyegrowth (i.e. potential treatment for hyperopia), according to certainembodiments. Higher order aberration in SNo addition to defocusMagnitude and sign of the higher order aberration 1 PSA only 0.30 μm =>PSA >= 0.125 μm 2 SSA only 0.30 μm => SSA > 0.075 μm 3 TSA only 0.30 μm=> TSA > 0.075 μm 4 QSA only −0.30 μm <= QSA <= −0.125 μm or 0.30 μm =>QSA > 0.075 μm 5 PSA & SSA −0.30 μm <= PSA <= 0.30 μm and 0.30 μm >=SSA > 0.075 μm 6 PSA & TSA −0.30 μm <= PSA <= 0.30 μm and (PSA/2) μm +0.075 μm <= TSA < 0.30 μm or −0.30 μm <= TSA < (PSA/2) μm − 0.075 μm 7PSA & QSA −0.30 μm <= PSA <= 0.30 μm and QSA in the range −0.20 to 0.20μm but excluding values where QSA = (|PSA|/3) μm +/− 0.075 μm 8 PSA,SSA, TSA −0.30 μm <= PSA < −0.05 μm & 0.05 μm < PSA < 0.30 μm; 0.075 μm<= SSA < 0.30 μm; −0.20 μm <= TSA < −0.025 μm & 0.025 μm < TSA < 0.20μm; 9 PSA, SSA, TSA and QSA −0.30 μm <= PSA < −0.05 μm & 0.05 μm < PSA <0.30 μm; 0.075 μm <= SSA < 0.30 μm; −0.20 μm <= TSA < −0.025 μm & 0.025μm < TSA < 0.20 μm; −0.20 μm <= QSA < −0.025 μm & 0.025 μm < QSA < 0.20μm;

Accordingly, when designing a lens, optical device or method of alteringthe eye, the aberrations may be selected to provide a combination of theaforementioned aberrations that provide for either a protective effectagainst eye growth for example for myopia, or which encourage eye growthfor example for hyperopia. The combination of aberrations may be appliedin combination with the required correction of any myopic defocus orhyperopic defocus.

From the foregoing description, it is apparent that the sphericalaberration terms, including the primary, secondary, tertiary andquaternary SA terms influence RIQ and through focus RIQ. In addition, ithas been found that much higher orders of spherical aberration may alsoinfluence RIQ and through focus RIQ. In various embodiments differentcombinations of spherical aberration are used, including embodimentsusing combinations of two or more spherical aberration terms thatprovide a required or acceptable through focus RIQ profile, togetherwith a required or acceptable RIQ at a particular focal length (e.g.distance vision). In certain embodiments, characterizations of one ormore of the spherical aberrations may also be used.

Section 6: The Instantaneous Gradient of the Image Quality

The foregoing description of stimulus for eye growth can be explainedunder an optical feedback mechanism that is based on the location of apeak on-axis RIQ. In certain examples, another alternative approachconsidered to describe the stimulus for eye growth is via the slope ofTFRIQ at the retina. In some embodiments, lenses, methods and/or devicesutilise the gradient or slope of the RIQ to control myopia progression,with or without astigmatism. In other embodiments, lenses, methodsand/or devices utilise the gradient or slope of the RIQ to treathyperopia, with or without astigmatism. The gradient or slope of RIQ maybe considered for one or more of the following variants of RIQ: a)monochromatic RIQ with or without considering effect of accommodation,b) polychromatic RIQ with or without considering effect ofaccommodation, c) global RIQ, d) RIQ considered with myopic impetus timesignal, e) global RIQ with myopic impetus time signal, each of which isdescribed herein.

In certain embodiments, the lenses, devices and/or methods disclosedherein may be applied to provide stimulus under this optical feedbackmechanism explanation of emmetropisation. Embodiments for addressing eyegrowth under the optical feedback explanation of emmetropisation (e.g.to address myopia progression or to seek to stimulate eye growth tocorrect hyperopia) may use aberrations to affect one, two or more of thelocation of the minima, or substantial minima, of the function Srelative to the retina and the gradient of the function S through theretina.

In the following description it is assumed that a positive measure ofthe gradient of the TFRIQ (increasing RIQ posterior to the retina)provides a stimulus for the development and progression of myopia, whilea negative measure of the same retards or halts myopia progression. FIG.14 is an exemplary that shows a plot of RIQ for two different cases,1402 and 1404, as a function of through focus in the direction posteriorto the retina, according to certain embodiments. The cases are twodifferent combinations of PSA, SSA and TSA that produce identical, orsubstantially identical, retinal RIQ. As can be seen from the figure,although both sets of selected aberrations produce similar image qualityat the retina (defocus=0), with the introduction of defocus (in thedirection of eye growth) the retinal image quality of test case 1402ramps up indicating stimulus for eye growth, while test case 1404indicates that there would be no stimulus for growth, as the retinalimage quality degrades further in the direction of eye growth.

From the results described herein that indicate the effects of HOA onimage quality and the resulting progression of myopia, it is possible todetermine the relevant HOA combinations that may be used in lenses,optical devices, and/or effected using optical surgery, which, whererelevant in combination with the eye's aberrations, may result in theHOA combinations that inhibit or retard eye growth for the treatment ofmyopia progression. In order to slow down eye growth in myopia,compensating optical devices and/or surgical procedures may be usedthat, in combination with the optics of the eye, may result in acombination of HOA that results in a negative gradient of TFRIQ, asshown in example 1404 (FIG. 14). For treating hyperopia in certainapplications, compensating optical devices and/or surgical proceduresmay be used that, in combination with the optics of the eye, may resultin a combination of HOA that results in a positive gradient of TFRIQ, asshown in example 1402 (FIG. 14).

If an aberration profile has a varying RIQ across a through focus range,then the slope of through focus RIQ at a particular focal length may bechanged by selecting a suitable defocus term C(2,0) with the consideredRIQ profile. For example, if the slope is positive at a first level ofthrough focus and negative at a second level of through focus, the slopeat the retina of a recipient eye may be selected by selectivelyintroducing defocus at either the first or second level. Examples ofaberration profiles that have varying RIQ slopes at different levels ofdefocus are provided herein in relation to embodiments of aberrationprofiles for application to presbyopia. Many of the embodimentsdescribed for presbyopia may be applied to provide a stimulus to retardand/or encourage eye growth under the optical feedback explanation ofemmetropisation described herein. Typically, younger people haveprogressing myopia and as such they may not be experiencing presbyopia.Accordingly, the aberration profile selected may place less weight onachieving high RIQ over a large through focus range and more weight onachieving the highest RIQ at the retina for distance vision incombination with providing a negative slope RIQ profile through theretina (i.e. decreasing RIQ in the direction of eye growth). For theyoung hypermetropes, again, the selected aberration profile may placeless weight on achieving high RIQ over a large through focus range andmore weight on achieving the highest RIQ at the retina for distance incombination with provision of a positive slope of RIQ profile behind theretina (in the direction of eye growth).

In certain embodiments, a lens, device and/or method may incorporate anaberration profile that provides, i) an acceptable on-axis RIQ; and ii)a through-focus RIQ with a slope that degrades in the direction of eyegrowth; to an eye with progressing myopia or an eye that is identifiedas at risk of developing myopia. In certain embodiments, the measure ofacceptable on-axis RIQ can be considered from one or more of thefollowing: on-axis RIQ of 0.3, on-axis RIQ of 0.35, on-axis RIQ of 0.4,on-axis RIQ of 0.45, on-axis RIQ of 0.5, on-axis RIQ of 0.55, on-axisRIQ of 0.6, on-axis RIQ of 0.65, or on-axis RIQ of 0.7. In certainembodiments, the candidate myopia eye may be considered with or withoutastigmatism.

In certain embodiments, a lens, device and/or method may incorporate anaberration profile that provides, i) an acceptable on-axis RIQ; and ii)a through-focus RIQ with a slope that improves in the direction of eyegrowth; to an eye with hyperopia. In certain embodiments, the measure ofacceptable on-axis RIQ can be considered from one or more of thefollowing: on-axis RIQ of 0.3, on-axis RIQ of 0.35, on-axis RIQ of 0.4,on-axis RIQ of 0.45, on-axis RIQ of 0.5, on-axis RIQ of 0.55, on-axisRIQ of 0.6, on-axis RIQ of 0.65, or on-axis RIQ of 0.7. In certainembodiments, the candidate hyperopic eye may be considered with orwithout astigmatism. In certain embodiments, the gradient or slope ofRIQ may be considered for one or more of the following variants of RIQ:a) monochromatic RIQ with or without considering effect ofaccommodation, b) polychromatic RIQ with or without considering effectof accommodation, c) global RIQ, d) RIQ considered with myopic impetustime signal, e) global RIQ with myopic impetus time signal, each ofwhich is described herein.

In certain embodiments, the slope across a range of field angles may beconsidered and/or variations in the RIQ for a range of pupil sizes. Forexample, an aberration profile may be selected that provides an averagemode, or substantially uniform slope, across a range of field angles,such as 10, 20, 30 or 40 degrees that either inhibits or encourages eyegrowth (and/or cancel existing aberrations in the eye that encourage orinhibit eye growth respectively). The average slope across the range ofpupil sizes or at the mode pupil size may also be considered.Alternatively, the design may be selected that has either a positive ornegative slope of through focus RIQ for field angles within a rangeand/or for pupil sizes with a range.

In some embodiments, an image quality produced by a lens and/or deviceat its focal distance is computed without the use of a model eye. Theimage quality produced by a lens and/or device may be calculatedanterior and/or posterior to the focal distance of the lens and/ordevice The image quality anterior and/or posterior to the focal distancemay be referred to as through focus image quality. The through-focusrange has a negative and a positive power end relative to the focaldistance. For example, in a through-focus range of −1.5 D to +1.5 D,−1.5 D to 0 D is considered as negative power end, while 0 D to +1.5 Dis considered as the positive power end. In some embodiments, thethrough-focus slope along the negative power end may be considered whilein other embodiments, the through-focus slope along positive power endmay be considered.

Section 7: Aberration Design or Selection Process

In some embodiments, determining the aberration profile required in alens, optical device and/or resulting from a procedure includes firstidentifying the HOA present in the eye. In some embodiments, determiningthe characterization of the aberration profile required in a lens,optical device and/or resulting from a procedure includes firstidentifying the HOA present in the eye. Measurements may be taken, forexample, using wavefront eye exams that use aberrometry such as with aShack-Hartmann aberrometer. The eye's existing HOA may then be takeninto account. In addition, one or more HOA effects inherent in thelenses or optical devices may also be taken into account.

When the requirement is for a lens that provides stimulus for eye growthor to retard eye growth, these existing HOA are then compared to HOAcombinations that inhibit or retard myopia progression (for example asdiscussed above with reference to FIGS. 5 to 14) to determine one ormore additional HOA that may be required to reduce or retard orencourage eye growth under the optical feedback mechanism ofemmetropisation. These additional combinations are then implemented inthe design of lenses or optical devices or implemented using opticalsurgery. Flowcharts in FIGS. 15 and 16 provide a summary of suitablemethods, according to certain embodiments.

Alternatively, in certain applications, the eye's existing aberrationsmay be disregarded and an aberration profile that provides the requiredthrough focus RIQ slope may be provided for the eye by a lens, Incertain applications a removable lens so that different aberrationprofiles may be trialled if required. The aberration profile resultingfrom the combination of the aberration profile of the lens and the eyemay then be measured to determine if the RIQ characteristics areacceptable (for example, provide a particular through focus RIQ slopeand acceptable RIQ for distance vision). Alternatively, different lensesmay be placed on the eye with measures of objective and/or subjectivevision determining which lens to select. Where the lens is selected toprovide stimulus inhibiting or encouraging eye growth without regard tothe eye's existing aberrations, the selected aberration profile may beone with generally higher values of spherical aberration, so that thesign of the slope is not changed by lower level of HOA in the eye. Incertain applications, the goal of the optimisation routine of the meritfunction in search of combination of HOA may be different. For example,when considering presbyopia the goal may be a combination of aberrationsthat provide high RIQ over a large through focus range. Where peripheralvision is useful, then the objective may include high RIQ over a largerange of field angles. Accordingly, in various embodiments the HOAs areutilised to optimise for the goals of a combination of high RIQ at theretina and one or more of a low slope through focus RIQ, a low change inRIQ with pupil diameter and a high RIQ in the peripheral field.

In certain applications, an acceptable high RIQ is considered to be anRIQ above 0.7, above 0.65, above 0.6, above 0.55, above 0.5, above 0.45,above 0.4, above 0.35, or above 0.3. In certain applications, anacceptable low change in RIQ with pupil diameter may be considered thechange in one or more of the following ranges: RIQ change between 0 and0.05, between 0.05 and 0.1, or between 0.1 and 0.15. In certain otherapplications, an acceptable low slope of through focus RIQ may beconsidered from one or more of the following: slope of less than zero,slope of equal to zero, slope of greater than zero, slope of about zero,slope ranging from −0.5 to zero, slope ranging from 0 to 0.5, sloperanging −1 to zero, slope ranging 0 to 1, slope ranging −1 to −0.5, orslope ranging 0.5 to 1. The high RIQ, low change in RIQ and low slope ofTFRIQ provided may be combined in or more combinations. For example, thecombination of a high RIQ of 0.40 or above, a low change in RIQ withpupil diameter between 0 and 0.05 and low slope of TFRIQ of about zeromay be applied to certain embodiments. In other applications, thecombination of a high RIQ of 0.3 or above, a low change in RIQ withpupil diameter between 0 and 0.075 and the low slope of TFRIQ rangingfrom −0.25 to 0.25 or −0.5 to 0.5 may be applied.

The examples that follow have been selected using the RIQ measure inEquation 2. The initial set of designs for analysis was found bycomputing this RIQ for all, or for a substantially number of,combinations of SA Zernike coefficients up to the 10th order. Thecoefficients used were constrained to the range −0.3 μm to 0.3 μm andconstrained to be a value that is a multiple of 0.025 μm. In certainembodiments, the RIQ used may be based on an approximation orcharacterization of Equation 2.

An analysis of the initial set of designs included: 1) identifyingoptimised combinations of Zernike coefficients that provide a high RIQand a negative slope through focus RIQ about the retina; 2)consideration of the RIQ and through focus RIQ and change in RIQ andthrough focus RIQ at different pupil sizes; and 3) consideration of theRIQ across the horizontal visual field. The relative weight given tothese stages of evaluation may vary for the particular recipient. Forthe purposes of identifying the following examples, most weight wasgiven to the first criteria.

Section 8: Examples of Optical Designs Addressing the Slope of ThroughFocus RIQ

Examples of designs for affecting stimulus for eye growth under anoptical feedback mechanism are provided herein. The examples below arerotationally symmetric. However, astigmatic designs and othernon-rotationally symmetric designs may be produced. When a deliberatedecentration of the symmetric designs is imposed so that the opticalaxes of the correcting contact lens coincides with a reference axis ofthe eye say pupillary axis or visual axis, some residual amounts ofasymmetric aberrations like coma and trefoil can be induced, these maybe compensated by the choice of additional higher order asymmetricterms. FIGS. 17 to 25 are exemplary that show the power profile graphsof sample designs that provide a RIQ that degrades in the direction ofeye growth for on-axis vision (i.e. at zero field angle), thus providinga stimulus to inhibit eye growth under the optical feedback mechanismexplanation of the emmetropisation process, according to certainembodiments. The aberration profile graphs are described as the axialpower variation in Dioptres across the optic zone diameter. The examplesprovided may have application to a progressing myope whose sphericalrefractive error is −2D and this information is indicated by a dual greyline on the power profiles.

FIG. 26 is an exemplary that shows the details of a sample design thatmay be used for hyperopia treatment, according to certain embodiments.This designs was produced by taking a specific aberration profile as aninput parameter that would produce a positive gradient of TFRIQ in thedirection of eye growth, as indicated in Table 2 and optimising thepower profile (front surface of correcting contact lens) to achieve arequired positive gradient. The lens design is described as the axialpower variation in Dioptres across the optic zone diameter. The exampleprovided may have application to a non-progressing hyperope whosespherical refractive error is +2D and this information is indicated by adual grey line on the power profile.

As explained herein, the example power profiles shown in FIGS. 17 to 26were selected based on the slope of RIQ around the retina, according tocertain embodiments. Across these examples, substantial variations inthe value of RIQ may occur. These variations occur on-axis, across thepupil diameter, and at different field angles. Additional selectioncriteria are the value of RIQ and the change in RIQ with field angle. Inparticular, the selection may be made to maximise one or more of RIQon-axis, across the pupil diameter (with or without reduction in lightof the Stiles-Crawford effect) and at different field angles. Inaddition, the size of the pupil of the recipient may also be used as aselection criterion—e.g., a first aberration profile may better suit afirst recipient with a normal pupil size of 4 mm and a second aberrationprofile may better suit a second recipient with a normal pupil size of 5mm. The ‘normal’ pupil size may optionally be selected having regard tolifestyle factors, such as the amount of time a person spends indoorsversus outdoors. Additional examples referred to below incorporate theseselection criteria. First however, to provide a point of comparison, theRIQ performance of a single vision lens is described and shown in FIG.27.

FIG. 27 is an exemplary that shows a graph of a measure of a throughfocus RIQ metric, according to certain embodiments, which in this case,and in the following examples, is visual Strehl Ratio (monochromatic).The RIQ may result, for example, from a single vision contact lens witha power of −2D used to correct a recipient model myopic eye with −2Donly. The horizontal (independent) axis shows the through focus, inDioptres. The zero (0) value on the horizontal axis represents thelocation of the focal point of the single vision lens and the vertical(dependent) axis shows the RIQ. Three plots are provided, one foron-axis (circles), one for a field angle of 10 degrees (triangles) andone for a field angle of 20 degrees (crosses).

As used in this example described herein, the term global is used torefer to consideration across a range of field angles, including zero.Thus, the graph shows Global through focus RIQ, as it includes plotsacross a range of field angles. While a single vision lens hassymmetrical RIQ on-axis at zero field angle, it has asymmetrical throughfocus RIQ at non-zero field angles, including both at 10 and 20 degrees.In particular, the graph shows that RIQ improves in the direction of eyegrowth at non-zero field angles, according to certain embodiments. Underthe optical feedback mechanism explanation of emmetropisation,peripheral as well as on-axis vision provides a stimulus for eye growth.In certain embodiments, the slope of the TFRIQ at the retina to controleye growth (negative slope, or decreasing RIQ for myopia and positiveslope, or increasing RIQ for hyperopia) may be across a range of fieldangles that may or may not include the zero or on-axis field angle. Anaverage measure of the slope of the TFRIQ (also referred to as theaverage through focus slope of the RIQ) may be used across a selectionof, or a range of, field angles. For example, slope of the TFRIQaveraged between at least −20° and +20° field angles. Another examplemay average the slope of the TFRIQ at at least −20°, 0° and +20° fieldangles. Broader field angles may also be used for example, between atleast −30° and +30° field angles or between at least −40° and +40° fieldangles.

In certain embodiments, the average slope of the TFRIQ across aselection of or a range of field angles may be a weighted average slopeof the TFRIQ that gives more, less or the same weight to different fieldangles to emphasise or weight the contributions of the different fieldangles according to the application.

FIG. 28 is an exemplary that shows a graph of RIQ for an embodiment of alens (named ‘Iteration A1’) selected to address the optical feedbackmechanism explanation of emmetropisation where eye growth is to bediscouraged (e.g. to address progressing myopia or to address a risk ofdeveloping myopia), according to certain embodiments. The data for FIG.28 was prepared for a pupil size of 4 mm and to address the same, orsubstantially the same, level of myopia as for the Single VisionIteration. Comparing FIG. 28 with FIG. 27, the RIQ no longer improves ina direction of eye growth for non-zero field angles. In particular, theRIQ has a strong trend towards degrading in the direction of eye growthfor 10 degrees off-axis. While there may be a slight improvement or nosubstantially no change in RIQ about the retina at 20 degrees off-axis,the overall effect is strongly biased towards degrading RIQ in thedirection of eye growth. FIG. 29 shows a power profile that result inthe RIQ graph of FIG. 28.

FIG. 30 is an exemplary that shows a graph of RIQ for certainembodiments of a lens (Iteration A2) selected to address the opticalfeedback mechanism explanation of emmetropisation. The data for FIG. 30was prepared for a pupil size of 5 mm.

FIGS. 31 and 32 are exemplary that show graphs of the RIQ for two otherembodiments of a lens (Iteration C1 and Iteration C2 respectively)selected to address the optical feedback mechanism explanation ofemmetropisation, but in this case to provide improving RIQ in thedirection of eye growth (e.g. to provide a stimulus to an eye to grow tocorrect hyperopia). FIGS. 31 and 32 show exemplary embodiments selectedwith different weights to the selection criteria. In the power profilethat gives FIG. 31, achieving a high on-axis RIQ was given more weightthan achieving a high RIQ across a large range of field angles.

In the power profile that gives FIG. 32, more weight was given toproviding a high RIQ across a large range of field angles than toachieving a high RIQ on-axis. In certain applications, an acceptablehigh RIQ across a large field angles is considered to be an RIQ above0.6, above 0.55, above 0.5, above 0.45, above 0.4, above 0.35, or above0.3. Table 3 lists the defocus and higher order aberrations coefficientsup to 20th order, in microns, over a 5 mm pupil diameter for the abovedescribed power profiles.

TABLE 3 Defocus and higher order Spherical aberration coefficients overa 5 mm pupil for a single vision lens and four exemplary embodimentswith a required slope for through focus RIQ. Iteration C(2,0) C(4,0)C(6,0) C(8,0) C(10,0) C(12,0) C(14,0) C(16,0) C(18,0) C(20,0) SingleVision −1.800 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 LensIteration A1 −1.568 0.107 −0.017 −0.016 −0.022 −0.008 0.026 0.005 −0.0160.003 Iteration A2 −1.562 0.115 −0.011 −0.011 −0.019 −0.007 0.025 0.004−0.017 0.005 Iteration C1 1.468 −0.135 0.020 0.029 0.036 0.011 −0.036−0.008 0.022 −0.003 Iteration C2 1.468 −0.116 0.035 0.010 −0.013 −0.030−0.014 0.025 0.004 −0.016

Section 9: Application to Presbyopia

Presbyopia is a condition where with age an eye exhibits a progressivelydiminished ability to focus on near objects. The ability to focus onnear objects may be referred to as accommodative ability. Pre-presbyopiais an early stage at which patients begin to describe symptoms ofdiminished ability to focus on near objects. The ability to focus onnear objects without use of lenses and/or devices disclosed herein isconsidered as a non-presbyopic condition. Certain embodiments aredirected to providing lenses, devices and/or methods that are configuredsuch that the embodiments provide visual performance that issubstantially comparable to the visual performance of a pre-presbyope ornon-presbyope over a range of distances with minimal ghosting.

For example, where the near distance is the range of 33 cm to 50 cm or40 cm to 50 cm; intermediate distance is the range of 50 cm to 100 cm,50 cm to 80 cm or 50 cm to 70 cm; and far distance is the range of 100cm or greater, 80 cm or greater or 70 cm or greater. Other distances orrange of distances may also be used.

In certain applications, extending the through focus RIQ may provide oneor more benefits in the context of presbyopia. The reduced ability ofthe eye to see at near due to the reduced accommodation may be partiallycompensated and/or mitigated by using the extended through focus ofcertain approaches described herein. The benefits may include visualperformance at near close to or approaching the visual performance of aproperly prescribed single-vision lens for near.

Other benefits may include (i) visual performance at far andintermediate distances substantially equivalent to the visualperformance of a properly prescribed single-vision lens for far visualdistance; (ii) visual performance over intermediate and far distancesthat is at least substantially equivalent to the visual performance of acorrectly prescribed single-vision lens at the far visual distance;(iii) visual performance, along a range of substantially continuousvisual distances, including intermediate and far distances, wherein thevisual performance of the multifocal lens is at least substantiallyequivalent to the visual performance of a correctly prescribedsingle-vision lens at the far visual distance; and/or (iv) providingvisual performance at far and intermediate distances substantiallyequivalent to the visual performance of a properly prescribedsingle-vision lens at the far visual distance with minimal, orsubstantially minimum, ghosting. In certain embodiments, the visualdistance over one or more of the following ranges i.e. near intermediateand far distances may be continuous, substantially continuous orcontinuous over a portion of the near distance or distances, theintermediate distance or distances, or far distance or distances. Thismay also be true for optical infinity. In certain embodiments,continuous may be defined as near distance range from 33 cm to 50 cm, 40cm to 50 cm or 33 to 60 cm; intermediate distance range from 50 cm to100 cm, 50 cm to 80 cm or 50 cm to 70 cm; and far distance range from100 cm or greater, 80 cm or greater or 70 cm or greater. According tocertain disclosed lenses, the lens is configured to provide the visualperformance, along continuous visual distances, including neardistances, intermediate distances, and far distances.

In some embodiments the through focus RIQ is extended further by takinga monocular optimisation approach, or using one or more of the monocularmethods disclosed herein. The monocular optimisation approach in certainembodiments is achieved by extending the through focus RIQ to optimiseone eye for distance vision and the other eye for near. In certainembodiments, this optimisation is by selecting different base powers(i.e. effective refractive prescriptions) for the lenses. The extendedthrough focus (for example RIQ) for each lens allows the base powers tobe separated, or used without sacrificing, or substantially reducing,far, intermediate, or near vision between the two base powers.

In certain embodiments, one or more of the monocular methods disclosedherein may be used to extend the binocular through-focus RIQ, or thethrough-focus RIQ, by using an aberration profile for one eye and adifferent aberration profile for the other eye. The extendedthrough-focus RIQ of each lens optimises one eye for distance vision andthe other eye for near without substantially reducing, far,intermediate, and/or near vision, and minimal, or substantially minimal,ghosting with the two aberration profiles.

In certain embodiments, one or more of the monocular methods disclosedherein may be used to extend the binocular through-focus RIQ, or thethrough-focus RIQ, by using an aberration profile and a base power forone eye and a different aberration profile and a different base powerfor the other eye. The extended through-focus RIQ of each lens optimisesone eye for distance vision and the other eye for near withoutsubstantially reducing, far, intermediate, and/or near vision, andminimal, or substantially minimal, ghosting with the two aberration andbase power profiles.

Under the monocular approach, in some embodiments, selection of anaberration profile may give a higher priority to the consideration ofthe RIQ and through focus RIQ, and change in RIQ and through focus RIQat different pupil sizes (which reflect the change in the eye withdifferent accommodation levels and illumination levels).

Similarly, a lens or optical device may be designed as a bifocal ormultifocal or omnifocal lens, with one or both of the partsincorporating aberration profiles as described herein to extend TFRIQ. Acombination of bifocal, multifocal, omnifocal lenses, devices, methodsand procedures can be used either in one eye or synergistically in botheyes by appropriate selection for each eye that will enhance thebinocular performance. For example, one eye may be biased for optimalvision for far and the other eye for optimal vision at near.

A combination of bifocal, multifocal, omnifocal lenses, devices and/orthe monocular method that may increase visual performance over a rangeof dioptric distances by about 1, 1.25, 1.5, 1.75, 2, or 2.25D. Forexample, with reference to such method of prescribing bifocal lenses:one eye may have far distance vision in the upper quadrants ofperformance (RIQ about 0.35, 0.4, 0.45, 0.5 or another selected) andnear vision in the lower quadrants of performance (RIQ about 0.1, 0.12,0.15, 0.17, 0.2 or another selected) and the other eye may haveintermediate vision in the upper quadrants of performance (RIQ about0.35, 0.4, 0.45, 0.5 or another selected) and near vision in the lowerquadrants of performance (RIQ about 0.1, 0.12, 0.15, 0.17, 0.2 oranother selected).

When different base powers, power profiles or aberration profiles areused in two different eyes; the different base powers, power profiles,aberration profiles may be selected so that the through focus RIQoverlaps to increase the binocular through-focus RIQ. For example, incertain embodiments, the base powers may be selected so that incombination the visual Strehl Ratio does not drop below 0.1, 0.15, 0.2,0.25, 0.3, 0.35, 0.40 or another selected value, between the combinedRIQ profiles.

(A) Examples for Presbyopia

FIG. 36 shows a graph of through focus RIQ (in this case visual StrehlRatio) for seven power profiles, according to certain embodiments. Inthis figure the vertical axis (RIQ) is defined on a logarithmic scale.FIG. 36 was obtained for a 5 mm pupil size and an eye with no myopia orhyperopia and no other higher order aberrations. One or more powerprofiles may be adapted to a myopic or hyperopic eye by incorporating anappropriate correcting defocus term, which does not affect the higherorder aberrations defining the power profiles used for form FIG. 36.

The seven power profiles are: a power profile that may appear in aconventional centre-distance aspheric multifocal lens (indicated bytriangles in FIG. 36); a power profile that may appear in a conventionalcentre-near multifocal lens (indicated by ‘x’ in FIG. 36); a powerprofile that may appear in a centre-distance concentric bifocal lens(indicated by filled ‘□’ in FIG. 36); a power profile that may appear ina centre-near concentric bifocal lens (indicated by empty ‘⋄’ in FIG.36) and three iterations (Iteration B1, Iteration B2, Iteration B3)including a favourable combination of spherical aberration (indicated byfilled circles, bold ‘+’ signs and a concentric circle pairs,respectively, in FIG. 36).

The power profiles for each of these are shown in FIGS. 37 to 43. Thecentre-distance and centre-near aspheric multifocals had the centrecomponent extend to about 2 mm and the outer zone power commence at aradius of about 1.8 mm. A linear transition was provided between thenear and distance power zones. The concentric bifocals both had a ringstructure, alternating between an additional power of 2 Dioptres and noaddition power (also referred to as base distance power).

Table 4 lists the defocus and higher order spherical aberrationcoefficients up to 20^(th) order, in microns, over a 5 mm pupildiameter, for the three exemplary embodiment power profiles, namely:Iteration B1 (FIG. 41), Iteration B2 (FIG. 42) and Iteration B3 (FIG.43), respectively.

TABLE 4 Defocus and Spherical aberration coefficients of three exemplaryembodiments for presbyopia. Iteration Iteration B1 Iteration B2Iteration B3 C(2,0) −0.096 −0.092 0.033 C(4,0) −0.135 0.032 0.003 C(6,0)0.02 0.074 0.077 C(8,0) 0.029 −0.015 −0.045 C(10,0) 0.036 −0.006 −0.023C(12,0) 0.012 −0.018 0.01 C(14,0) −0.036 −0.009 0.014 C(16,0) −0.010.007 0.007 C(18,0) 0.022 0.011 0.003 C(20,0) 0 0.002 −0.014

Table 5 lists out the defocus and higher order spherical aberrationcoefficients up to 20^(th) order, in microns, over a 5 mm pupildiameter, for the described power profiles, namely, centre-distanceaspheric multifocal (FIG. 37), and centre-near aspheric multifocal (FIG.38, respectively.

TABLE 5 Defocus and Higher order spherical aberration coefficients ofboth centre-distance and centre-near type aspheric multifocal lenses.Centre-Distance Centre-Near Iteration aspheric multifocal asphericmultifocal C(2,0) 1.15 0.324 C(4,0) 0.181 −0.244 C(6,0) −0.09 0.114C(8,0) 0.02 −0.021 C(10,0) 0 −0.013 C(12,0) 0 0.011 C(14,0) 0 0 C(16,0)0 0 C(18,0) 0 0 C(20,0) 0 0

In the aspheric multifocal lenses the spherical aberration coefficientsprogressively decrease in absolute magnitude with an increase in order.This is in contrast to the power profiles of Iteration B1, Iteration B2and Iteration B3, which include at least one higher order sphericalaberration term with an absolute value coefficient greater than theabsolute value of the coefficient for a lower order term. Thischaracteristic is present in one or more of the embodiments of powerprofile described herein. From FIG. 36, it can be noted that thecentre-distance aspheric multifocal has a RIQ of 0.23 at 0D, whichsubstantially inferior than the other power profiles, according tocertain embodiments. However, performance of this lens as gauged by theRIQ metric is maintained relatively constant over a large through focusrange. For example, at −0.4 Dioptres the RIQ is about 0.2, at 0.67 theRIQ is about 0.18 and at −1 Dioptres, the RIQ is about 0.12.

The centre-near aspheric multifocal has a RIQ at 0D is about 0.5. Withthis exemplary design, the RIQ falls to about 0.24 at −0.67 Dioptres(still better than the centre-distance aspheric multifocal). However,beyond that the centre-near aspheric multifocal has a rapidly decreasingRIQ, as can be seen at −1 Dioptre the value of RIQ is about 0.08. Bothof the concentric bifocals (centre-distance and -near) have a low RIQ of0.13 and 0.21 at 0D. Both of the concentric bifocals maintain theirlevel of RIQ or better over a range of approximately 1.1 Dioptres.

TABLE 6 RIQ values for two bifocal lenses, two concentric bifocal lensesand three aberration profiles for extended through focus RIQ. Centre-Centre- Centre- Centre- Distance Near Distance Near Defocus Defocusaspheric aspheric Iteration Iteration Iteration concentric concentricshifted (D) multifocal multifocal B1 B2 B3 bifocal bifocal by +0.50−1.1085 0.1021 0.0601 0.1342 0.0918 0.0971 0.2025 0.1349 −0.6085 −0.99770.1212 0.0768 0.1831 0.1338 0.1228 0.2447 0.1524 −0.4977 −0.8868 0.14070.1062 0.2394 0.1882 0.1577 0.2913 0.1675 −0.3868 −0.7760 0.1598 0.15740.2957 0.2511 0.2095 0.3362 0.1789 −0.2760 −0.6651 0.1776 0.2383 0.34230.3160 0.2830 0.3700 0.1851 −0.1651 −0.5543 0.1931 0.3481 0.3867 0.42620.3723 0.3839 0.1855 −0.0543 −0.4434 0.2060 0.4699 0.4550 0.5318 0.45830.3735 0.1805 0.0566 −0.3326 0.2162 0.5715 0.4992 0.6099 0.5266 0.34170.1709 0.1674 −0.2217 0.2237 0.6185 0.5110 0.6451 0.5691 0.2969 0.15840.2783 −0.1109 0.2284 0.5913 0.4924 0.6369 0.5879 0.2495 0.1444 0.38910.0000 0.2304 0.4980 0.5014 0.5993 0.5906 0.2076 0.1300 0.5000 0.11090.2294 0.3702 0.4924 0.5511 0.5825 0.1754 0.1167 0.6109 0.2217 0.22490.2468 0.5110 0.5055 0.5609 0.1539 0.1055 0.7217 0.3326 0.2160 0.15490.4992 0.4648 0.5182 0.1418 0.0973 0.8326 0.4434 0.2048 0.1010 0.45500.4232 0.4513 0.1367 0.0924 0.9434 0.5543 0.2000 0.0758 0.3867 0.37410.3672 0.1358 0.0908 1.0543 0.6651 0.2173 0.0650 0.3082 0.3154 0.28150.1363 0.0917 1.1651 0.7760 0.2727 0.0588 0.2327 0.2511 0.2095 0.13620.0940 1.2760 0.8868 0.3701 0.0535 0.1694 0.1882 0.1577 0.1347 0.09621.3868 0.9977 0.4907 0.0491 0.1219 0.1338 0.1228 0.1325 0.0992 1.49771.1085 0.5962 0.0458 0.0896 0.0918 0.0971 0.1305 0.1087 1.6085

Iteration B1, Iteration B2 and Iteration B3 have at least as good RIQ at0D, as the centre near bifocal and also better RIQ across thethrough-focus range between −0.65D and 0.75D as the eye accommodates.For example Iteration B2 has an RIQ of about 0.53 at −0.4 Dioptres,about 0.32 at −0.67 Dioptres and about 0.13 at −1 Dioptres. Throughfocus performance (RIQ) of Iteration B1, Iteration B2 and Iteration B3can be further extended. This extension is achieved by shifting thecurves to the left in FIG. 36. However, the performance of thecentre-near aspheric multifocal lens, in this exemplary, cannot beshifted in this manner without substantially affecting performance, dueto the asymmetric RIQ that decreases substantially more rapidly for pluspowers (right hand side of FIG. 36).

For example, the three exemplary iterations have an RIQ of about 0.40 at+0.55D. Combining the spherical aberration terms with a +0.55D defocusterm will shift the RIQ value for distance vision to the value for+0.55D in FIG. 36. Considering Iteration B2 again, the through focusperformance (RIQ) would be modified as follows: an RIQ of about 0.4 atdistance vision, an RIQ of about 0.53 at −0.4 Dioptres, about 0.64 at−0.67 Dioptres, about 0.52 at −1 Dioptres, about 0.40 at −1.1 Dioptres,and about 0.15 at −1.5 Dioptres.

By shifting the distance vision point in a lens with combinations of HOAthat extend through focus RIQ performance, then the lenses, devicesand/or methods that provide the combination of HOA can have asubstantially improved through focus performance. This is achieved whilemaintaining at least as good RIQ as a centre near aspheric multifocaland substantially improved RIQ in comparison to a centre distanceaspheric multifocal. The amount of defocus plus power added to shift theRIQ curves is a matter of choice, representing a trade-off betweendistance vision RIQ and near vision RIQ. Table 6 shows the defocus(leftmost column) and RIQ values for the power profiles described above.It also shows the defocus values shifted by +0.55D, applicable when toIteration B1, Iteration B2 and/or Iteration B3 is modified by thisamount.

FIG. 115 plots the through-focus retinal image quality for fiveexemplary combinations with higher order aberrations (T1 to T5 shown inthe table 6.1) that include only symmetric higher order aberrations. Thethrough-focus retinal image quality computed for the five exemplaryhigher order aberrations combinations using the monochromatic RIQ(visual Strehl ratio) described in the equation 2. The combinations T1,T4 and T5 used a 3 mm pupil diameter to obtain the through-focus retinalimage quality while the combinations T2 and T3 used a 4 mm pupildiameter. These computations for a specific pupil diameter and/or withspecific retinal image quality result in exemplary combinations. Otherexemplary combinations are also contemplated using one or more of thefollowing: image quality metrics, pupils, spatial frequency ranges tocalculate the through focus retinal image quality.

Q-metric Visual Strehl Visual Strehl Visual Strehl Visual Strehl VisualStrehl ratio ratio ratio ratio ratio Pupil 3 mm 4 mm 4 mm 3 mm 3 mm SF 0to 30 c/d 0 to 30 c/d 0 to 30 c/d 0 to 30 c/d 0 to 30 c/d CoefficientsAberration Aberration Aberration Aberration Aberration coefficients ofcoefficients of coefficients of coefficients of coefficients ofembodiment embodiment embodiment embodiment embodiment T1 T2 T3 T4 T5C(2,0) 0.426 0.907 0.56 0.357 0.181 C(4,0) −0.116 −0.112 −0.096 −0.092−0.096 C(6,0) −0.012 0.049 0.038 −0.061 −0.005 C(8,0) −0.040 0.058 0.0190.028 −0.021 C(10,0) −0.016 −0.111 −0.084 0.04 0.014 C(12,0) 0.042−0.049 −0.024 −0.012 0.028 C(14,0) 0.012 0.063 0.055 −0.017 −0.013C(16,0) −0.027 −0.005 −0.007 0.007 −0.011 C(18,0) 0.012 −0.02 −0.020.003 0.012 C(20,0) 0 0.017 0.016 −0.001 −0.005

Table 6.1 shows the higher order aberration coefficients of symmetricaberrations, represented in a Zernike polynomial described up to 20thorder, for five exemplary embodiments, T1 to T5.

(B) Effect of Pupil Size

FIGS. 44 to 46 show the variation in through focus RIQ with pupil sizefor Iteration B1, Iteration B2 and Iteration B3 respectively, accordingto certain embodiments. The exemplary RIQ profiles are relativelystable, in that the RIQ retains the combination of a relatively high RIQ(in comparison to, for example, a centre distance aspheric multifocal)in combination with a relatively long through focus range (in comparisonto, for example, a centre near aspheric multifocal). Figure sets 47, 48and 49, 50 show the variation in through focus RIQ with pupil size forthe two concentric bifocals and two aspheric multifocals, respectively.From these figures it can be seen that, comparatively, the change in RIQand through focus RIQ performance is less stable for these lenses thanIteration B1 (FIG. 39), Iteration B2 (FIG. 40) and Iteration B3 (FIG.41). FIGS. 39 to 50 are examples, according to certain embodiments.

(C) Monocular and/or Binocular Design

As described herein, Iteration B2 (FIG. 40) may provide an RIQ of 0.4 orabove from distance vision to about an intermediate vergence of about1.1 Dioptres. When appropriate level of defocus is added to the sameiteration while correcting the other eye, TFRIQ can be extended from 1.1Dioptres to up close, say 2.2D target vergence, i.e. binocularlycombined the candidate eye may maintain an RIQ of 0.4 or above fromdistance test distance to all the way up to, or substantially up to 2.2Dioptres. Using this monocular design approach and assuming therecipient accepts the monocular design, the combined through focusperformance is substantially extended, according to certain embodiments.

Referring to the through focus profiles shown in FIGS. 51 and 52, whichare described herein, under the monocular design approach, one lens willbe selected to have a base power (distance refractive prescription) thatshifts the through focus curve to the extreme, or subs left (starting at−2.5D mark) and the other lens selected to have a base power that shiftsthe through focus curve slightly to the left (starting at −1.5D mark),according to certain embodiments.

FIGS. 51 and 52 show the TFRIQ of the design of two pairs of powerprofiles (Binocular ‘Q’ correction), according to certain embodiments.Each lens in the pair has been designed to extend RIQ in combinationwith the other lens in the pair. The defocus and higher order sphericalaberration coefficients for these combinations are specified in Tables 7and 8 respectively.

TABLE 7 Defocus and higher order spherical aberration coefficients offirst exemplary embodiment for monocular design of lenses for presbyopia(Effective add of 1.5D in the negative direction of through-focus curve.Combination Right Eye Left Eye C(2,0) 0.28 0.57 C(4,0) −0.1 0.125 C(6,0)0.025 −0.075 C(8,0) 0.075 −0.075 C(10,0) 0.025 −0.025 C(12,0) 0.025 0C(14,0) 0.025 0.025 C(16,0) 0.025 0.025 C(18,0) 0.025 −0.025 C(20,0) 0−0.025

TABLE 8 Defocus and higher order spherical aberration coefficients ofsecond exemplary embodiment for monocular design of lenses forpresbyopia (Effective add of 2.5D in the negative direction ofthrough-focus curve. Combination Right Eye Left Eye C(2,0) 0.433 0.866C(4,0) −0.1 −0.1 C(6,0) −0.05 −0.05 C(8,0) 0.025 0.025 C(10,0) 0.0250.025 C(12,0) −0.025 −0.025 C(14,0) −0.025 −0.025 C(16,0) 0 0 C(18,0) 00 C(20,0) 0 0

The power profiles described in relation to Table 7 and Table 8 areexamples of combinations of higher order aberrations that provideenhanced through-focus performance on the negative side of thethrough-focus function. Similarly, using this monocular design approach,the combined through-focus performance can also be substantiallyextended on the right side of the through-focus function, provided anappropriate level of defocus is added to a selected combination ofhigher order aberrations. FIGS. 53 and 54 show examples with arelatively constant RIQ (>0.35) over a range of defocus, in the positivedirection of the through-focus function, according to certainembodiments. The defocus and higher order spherical aberrationcoefficients for these combinations are specified in Tables 9 and 10,respectively.

TABLE 9 Defocus and higher order spherical aberration coefficients ofthird exemplary embodiment for monocular design of lenses for presbyopia(Effective add of 1.5D in the positive direction of through-focuscurve). Combination Right Eye Left Eye C(2,0) −0.28 −0.43 C(4,0) −0.125−0.125 C(6,0) −0.05 −0.05 C(8,0) 0.075 0.075 C(10,0) 0.025 0.025 C(12,0)−0.025 −0.025 C(14,0) 0 0 C(16,0) 0 0 C(18,0) 0 0 C(20,0) 0 0

TABLE 10 Defocus and higher order spherical aberration coefficients offourth exemplary embodiment for monocular design of lenses forpresbyopia (Effective add of 2.5D in the positive direction ofthrough-focus curve). Combination Right Eye Left Eye C(2,0) −0.43 −0.86C(4,0) −0.125 −0.125 C(6,0) −0.05 −0.05 C(8,0) 0.075 0.075 C(10,0) 0.0250.025 C(12,0) −0.025 −0.025 C(14,0) 0 0 C(16,0) 0 0 C(18,0) 0 0 C(20,0)0 0

FIG. 118 shows the through-focus retinal image quality for two exemplarydesigns, N41 and N42, which were computed at 3 mm pupil diameter usingvisual Strehl ratio as the retinal image quality metric, described insection 1. The power profiles of the exemplary embodiment pair, N41 andN42, as a function of half-chord diameter of the optic zone aredescribed in the FIG. 117. This pair of lenses may be prescribed for apair of eyes, where one design is prescribed for a selected eye and theother design is prescribed for the fellow eye. In this example, as seenin FIG. 118, the solid and the dual lines represents the through-focusretinal image quality for each of the two exemplary designs, N41 andN42, respectively. A pair of exemplary designs with differentperformance characteristics may be used in a method of correcting a pairof eyes. Using such exemplary methods may result in a coupling and/orsummation of the individual performances of each lens that may occur atthe visual cortex level in the brain. For example, a summated responsefor the embodiment pair, N41 and N42, is represented by the dashed linein FIG. 118.

FIG. 138 shows the through-focus retinal image quality for two exemplarydesigns, N11 and N12, which were computed at 3 mm pupil diameter usingvisual Strehl ratio with the inclusion of the cosine of the phasetransfer function as the retinal image quality metric, described insection 1. The power profiles of the exemplary embodiment pair, N11 andN12, as a function of half-chord diameter of the optic zone aredescribed in the FIG. 137. This pair of lenses may be prescribed for apair of eyes, where one design is prescribed for a selected eye and theother design is prescribed for the fellow eye. In this example, as seenin FIG. 138, the solid and the dual lines represents the through-focusretinal image quality for each of the two exemplary designs, N11 andN12, respectively. A pair of exemplary designs with differentperformance characteristics may be used in a method of correcting a pairof eyes. Using such exemplary methods may result in a coupling and/orsummation of the individual performances of each lens is expected at thevisual cortex level in the brain. For example, a summated response forthe embodiment pair, N11 and N12, is represented by the dashed line inFIG. 138.

Section 10: Design for Enhancing Central Vision

Some embodiments may be used to selectively optimise visual performanceunder one or more defined viewing conditions. Such viewing conditionsmay include but are not limited to specific viewing distances, specificlighting conditions, specific vision tasks or combinations thereof. Theoptical performance may include the retinal image quality metricsdescribed herein. With respect to the designs for enhancing centralvision, the visual performance may include visual acuity and/or contrastsensitivity. For example, utilising some of the disclosed embodiments,devices, lenses and/or methods may be produced that are selectivelyoptimised for one or more of the following: high contrast visual acuity,low contrast visual acuity, contrast sensitivity, high illumination, lowillumination, photopic (day time viewing), mesopic, scotopic (night-timeviewing), distance viewing, computer viewing, reading at near orcombinations thereof.

Section 10.A: Design for Peripheral Field

In some embodiments, when selecting a combination of HOA to form a powerprofile, the weight given to peripheral vision may be increased. Thismay, for example, be applicable when the recipient plays certain sportsin which peripheral vision is important.

FIG. 55 shows a graph of RIQ (again visual Strehl Ratio), for threedifferent power profiles that substantially equalise RIQ across thehorizontal visual field, according to certain embodiments. The RIQmeasures were obtained for a 5 mm pupil. The defocus and higher orderspherical aberration coefficients for each power profile are shown inTable 11.

TABLE 11 Defocus and higher order spherical aberration coefficients ofthree exemplary embodiments for substantially constant RIQ over extendedhorizontal field angles Iteration Iteration A3 Iteration A4 Iteration A5C(2,0) −1.506 −1.504 −1.501 C(4,0) 0.111 0.114 0.117 C(6,0) −0.04 −0.037−0.034 C(8,0) −0.015 −0.013 −0.01 C(10,0) 0.007 0.009 0.012 C(12,0)0.025 0.027 0.029 C(14,0) 0.011 0.013 0.014 C(16,0) −0.025 −0.024 −0.023C(18,0) −0.003 −0.002 −0.002 C(20,0) 0.017 0.016 0.015

The Iterations A3 (FIG. 56), A4 (FIG. 57) and A5 (FIG. 58) produced anon-axis RIQ of about 0.5 across zero to 30 degrees field angle (ifhorizontal symmetry is assumed, that is 60 degrees in total across bothnasal and temporal fields), according to certain embodiments. The RIQon-axis is also about 0.5, which is lower than some other embodimentswhere degradation in RIQ below 0.5 with increasing field angle ispermitted.

Accordingly, in certain embodiments, the RIQ on-axis may be traded-offagainst RIQ at high field angles. For example, RIQ may be permitted todrop to 0.2 at 30 degrees field angle (but remain at 0.5 or above for 20degrees field angle and less), to allow a selection of HOA thatincreases on-axis RIQ above those shown in FIG. 55. Power profiledesigns for peripheral vision may be selected for a lens designed toprovide a slope of RIQ (providing stimulus to retard or encourage eyegrowth under the optical feedback mechanism explanation foremmetropisation), or correction/lenses for presbyopia (emmetropia,myopia or hyperopia) or for other eyes. In certain embodiments, highfield angles are one or more of the following: 10 degrees, 20 degrees,30 degrees or 40 degrees of the visual field. Other suitable highfield-angles may also be used in certain applications.

Section 11: Selection of Positive and Negative Phase

For a particular recipient of a lens, device and/or a method disclosedherein, a selection may be made between two power profiles of oppositephases. In this context, the term ‘opposite phase’ identifies powerprofiles that have identical, or substantially identical, magnitudes ofspecific combination sets of higher order aberrations over a desiredpupil, while their signs are opposite to each other. FIGS. 59 and 60show power profile iterations E1 and E2, which are examples of powerprofiles with opposite phases, according to certain embodiments. Table12 reflects the magnitudes and signs of the higher order sphericalaberration terms for iterations E1 and E2. The lenses of opposite phasedescribed herein may result in the same, or substantially the same,on-axis peak RIQ. The through focus RIQ performance of such phaseprofile pairs may be mirror images, or substantially mirror images, ofeach other across the Y-axis (i.e. shifted apart by defocus), as shownin FIG. 61. However, this would result if the inherent higher orderaberration profile is negligibly small (say for example primaryspherical aberration in the range of −0.02 μm to 0.02 μm over a 5 mmpupil).

TABLE 12 Defocus and higher order spherical aberration coefficients oftwo exemplary embodiments with opposite phases (i.e. mirror imaged powerprofiles across the X-axis). Iteration Iteration E1 Iteration E2 C(2,0)−2.015 −1.573 C(4,0) −0.102 0.102 C(6,0) 0.021 −0.021 C(8,0) 0.019−0.019 C(10,0) 0.025 −0.025 C(12,0) 0.01 −0.01 C(14,0) −0.025 0.025C(16,0) −0.006 0.006 C(18,0) 0.016 −0.016 C(20,0) −0.003 0.003

The interactions between the inherent aberration profiles of thecandidate eyes and a selected phase profile may either have a) animproved or b) degraded effect on the objective and/or subjectiveoptical and/or visual performance. As the TFRIQ is dependent on theinherent aberration profile, a phase profiles selected for instance maybe useful to change the slope of TFRIQ in the direction that wouldfavour the emmetropisation process for myopic or hyperopic eyes; oralternatively the same, or similar, phase profile may be used tomitigate the presbyopic symptoms in alternative candidate eyes.

FIGS. 62 and 63 show how the TFRIQ of opposite phase profiles aredependent on the inherent ocular aberration of the candidate eye (inthis example positive spherical aberration), according to certainembodiments. Certain embodiments disclosed herein involve providinglenses of the same, or substantially same, design, but opposite phaseand allowing the recipient to select the preferred phase. The process ofselection can be via an objective assessment of TFRIQ performance metricand/or could be purely a subjective preference via visually guidedtests.

Section 12: Combination Identification and Selection

As described herein for certain embodiments, it is possible to provide adesirable on-axis RIQ for distance and appropriate through focus RIQthat would enable better visual performance for distance, intermediateand near vergences by choosing an appropriate combination of HOA. Thiscombination of higher order aberrations may contain a correction for theinherent aberration profile of the test candidate. The Appendix A tothis specification lists 78 combinations of higher order sphericalaberration coefficients that provide both a usefully high RIQ and anoption to provide an extended through focus RIQ in the negativedirection (left hand side). Also shown in the Appendix A, as a point ofcomparison, is a combination which does not have spherical aberration,of any order. The Appendix B shows the TFRIQ values for the combinationslisted in the Appendix A. The calculations were performed for a pupilsize of 4 mm, however the approach, or method, may be extended to otherappropriate and/or desired pupil sizes if required or desired. Forexample, the method may be used with a pupil size within one or more offollowing ranges: 1.5 to 8 mm, 2 to 8 mm, 2.5 to 8 mm, 3 to 7 mm, 3 to 8mm and 3.5 to 7 mm. For example, the method may be used with pupil sizesof about 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5 or 8 mm.

The TFRIQ measures of the 78 aberration combinations are shown in FIG.64, the black line showing the symmetrical RIQ that has resulted from acombination that has no higher order aberrations, the lighter lines(i.e. grey lines) showing the enhanced performance in the negativedirection of the TFRIQ function for the 78 combinations that involvehigher order spherical aberration terms.

From FIG. 64, a number of observations can be made. The 78 profiles withhigher order spherical aberration terms provide an extended throughfocus performance in the negative direction, particularly when anappropriate selection of a negative power is made to shift the plottedthrough-focus profile towards negative defocus (left). The 78 profilesinclude a range over which RIQ is 0.1 or higher of at least 2 Dioptres.Several of the 78 profiles include a range over which RIQ is 0.1 orhigher of at least 2.25 Dioptres. The 78 profiles include an RIQ (visualStrehl Ratio—monochromatic) that peaks above 0.35. Many of the profilesinclude an RIQ that peaks above the thresholds of 0.4, 0.5, 0.6 and 0.7and some combinations result in a peak that lies above 0.8 mark.

The spherical aberration terms vary in the combinations, from one(example: combination 77) through to the nine. In other embodiments evenhigher orders of spherical aberration terms may be added, to createadditional combinations.

The combination 77 in the Appendix A shows that by selecting aparticular level of primary spherical aberration, the aberration profilemay be beneficially used for a presbyopic eye. See U.S. Pat. No.6,045,568 for myopia. In contrast, according to certain embodiments, astimulus to retard eye growth on-axis under the optical feedbackexplanation of emmetropisation is achieved if the retina is located onthe negative side of the graph shown in FIG. 65 (i.e. the focal lengthof the lens is longer than the eye). In other words, the aberrationprofile typically includes a C(2,0) term with further negative powerover the amount required to correct myopia.

Appendix C lists another 67 combinations of higher order coefficientsthat provide both a usefully high RIQ and an option to provide anextended TFRIQ in the positive direction (right hand side of FIG. 66).Also shown in Appendix C, as a point of comparison, is a combinationwhich does not have spherical aberration of any order. The Appendix Dshows the TFRIQ values for the combinations listed in Appendix C. Again,calculations were performed for a pupil size of 4 mm, however theapproach, or methods, may be extended to other appropriate or desiredpupil sizes, if required or desired.

The TFRIQ measures of the 67 aberration combinations are shown in FIG.66, the black line showing the symmetrical RIQ that has resulted from acombination that has no higher order aberrations, the lighter (i.e.grey) lines showing the enhanced performance in the positive directionof the TFRIQ function, for the 67 combinations that involved higherorder spherical aberration terms.

From the FIG. 66, a number of observations can be made. The 67 profileswith higher order spherical aberration terms provide an extendedthrough-focus performance in the positive direction particularly whenappropriate selection of a negative power is made to shift the plottedthrough-focus profile towards negative defocus (left). The 67 profilesinclude a range over which the RIQ is 0.1 or higher or greater than2.5D. FIG. 67 shows an example workflow diagram for identifying a powerprofile for application to a presbyopic eye, according to certainembodiments.

Section 13: Spherical Aberration and Astigmatism

Iterations B1, B2 and B3 have been described herein for emmetropicpresbyopia. When considering the astigmatic presbyopia, at least twodifferent methods can be adopted. A first method of correction iscompleted by considering astigmatic refractive error as an equivalentsphere. In this method, the spherical equivalent prescription is deducedby dividing the cylindrical/astigmatic power divided two (S=−C/2). Thisis a very common approach often considered to address low to moderateamounts of astigmatism, say up to −1.5D. Once the equivalent sphere isavailed, the same, or substantially the same, iterations describedherein, say for example B1, B2 or B3 can be used as an effectiveprescription, once the defocus term is adjusted to suit the sphericalequivalent.

A second method considers preparation of a toric prescription for bothastigmatism and presbyopia. FIG. 68 shows an exemplary embodiment thatincludes a toric power profile to treat both astigmatism and presbyopia.In this case, the prescription is made to correct an individual who hasan astigmatic correction of −1D @ 90 and requires an additional power toenable near viewing. As can be noted from the figure, the differencebetween the horizontal and vertical meridian is −1D, this magnitude isset to correct the astigmatism in the above case; while the higher orderspherical aberration combination is aimed to mitigate the presbyopicsymptoms. Other suitable methods may also be used or incorporated intosome of the disclosed embodiments.

The aberration profiles of some exemplary embodiments with substantiallyrotationally symmetric terms may be selected to mask and/or correctastigmatism up to at least −0.5 DC, −0.75 DC, −1 DC and −1.25 DC. Insome embodiments, the correction of astigmatism may not be dependent onthe axis of the astigmatism corrected. In some embodiments, the choiceof rotationally symmetric aberrations to mask and/or correct astigmatismmay be limited to at least 10th, 14^(th), 18^(th) or 20^(th) orderZernike polynomial expansion. In the current example, shown in Table12.1, the calculations were performed using 5 mm pupil, 0 to 25cycles/degree spatial frequency range and visual Strehl ratio as thethrough focus retinal image quality metric. However, other combinationsof pupil sizes, retinal image quality metrics and/or spatial frequenciesmay also be used for such computations.

TABLE 12.1 Defocus and higher order spherical aberration coefficients ofan exemplary embodiments which masks astigmatism of about −1.25DC at anyaxis. The computations were performed using visual Strehl ratio as theRIQ metric at 5 mm pupil diameter and a spatial frequency range of 0 to25 cycles/degree. Astigmatism introduced −1.25DC × 90 Pupil size 5Spatial Frequency 0 to 25 c/d Retinal image quality metric VSOTF Zernikecoefficients for the selected combination C(2,0) 0 C(4,0) −0.069 C(6,0)−0.002 C(8,0) −0.001 C(10,0) −0.063 C(12,0) −0.004 C(14,0) 0.075 C(16,0)0.027 C(18,0) −0.036 C(20,0) −0.023

Section 13.A: Applications to Vision Improvement

Some embodiments are directed to lenses, optical devices and/or methodscomprising the aberration profiles that are beneficial because theyimprove vision for seeing at certain levels of visual details; forexample, for visual details at a desired spatial frequency or a desiredrange of spatial frequencies. Improvement of vision may be in the formof improvement of retinal image quality, visual acuity, contrastsensitivity at a desired spatial frequency or a range of spatialfrequencies and/or combinations thereof.

Visual acuity may sometimes be used as a measure of an aspect of visualperformance. Visual acuity measurement evaluates the limit when a visualtarget, such as a letter, or a letter “E” (illiterate′ E) or a letter“C” (Landolt C), or some other target, may no longer be resolved,identified or correctly reported by the patient who is undertaking thevisual acuity measurement. The limit is related to, among other factors,the spatial frequency or spatial frequencies (how finely spaced thevisual target details are) of the visual target and the contrast of thevisual target. The limit of visual acuity may be reached when thecontrast of the image of the visual target, created by the optics of aneye with or without additional optical devices, is too low to bediscerned by the visual system (including the retina, visual pathway andvisual cortex). Since the retinal image contrast required for discerninga retinal image increases with increasing spatial frequency (i.e.contrast has to be greater for finer detailed targets), for targets of arange of fineness of details (or spatial frequencies), an eye, or eyewith optical devices typically is able to discern the highest spatialfrequency, or the finest details for which the contrast of the retinalimage is equal to or greater than the minimum contrast required fordetecting the details.

In some embodiments, one way by which visual acuity may be improved isto increase the contrast of the retinal image at the level of finenessof details (or spatial frequencies) near to and/or slightly greater than(i.e. finer details or higher spatial frequency) the visual acuity ofthe natural eye or eye with optical devices.

Certain embodiments are directed to aberration profiles that increasecontrast from slightly lower than or near to the visual acuity of anatural eye or a natural eye with conventional optical devices, to nearto or slightly higher than the visual acuity of the natural eye or thenatural eye with conventional optical devices.

In one exemplary embodiment, an eye may have a best-corrected visualacuity (i.e. the best visual acuity achievable using the best correctionusing conventional optical devices for its refractive error, which maybe myopia or hyperopia or astigmatism or some combinations thereof) of6/6 (or 20/20) acuity. This visual acuity level may be equated to aspatial frequency of 30 cycles per degree. That is, targets with finerdetails, and higher spatial frequencies, may be producing retinal imagecontrasts that are too low to be discerned by the retina and visualsystem. In this exemplary embodiment, shown in the FIG. 134, theoptimised aberration combination provides an enhanced (higher) contrastretinal image at the spatial frequency range of 20 cycles per degree to60 cycles per degree; that is, from slightly lower than thebest-corrected visual acuity of the exemplary eye (with the correcteddefocus terms and uncorrected higher order aberrations) to slightlyhigher than the best-corrected visual acuity of the exemplary eye. Theincreased contrast translates to an increase in RIQ for the exemplaryeye. With the increased contrast at this range of spatial frequenciesprovided by the higher order aberration of this exemplary embodiment,the exemplary eye may achieve better vision performance and/or improvedvisual acuity.

In yet another application, the eye may be amblyopic; i.e. sufferingfrom amblyopia. Amblyopia is a vision condition in which even with thebest optical correction, the eye is not able to attain visual acuitythat is usually attainable by normal eyes. An amblyopic eye may havevery low visual acuity such as 6/9 (i.e. 20/30), 6/12 (i.e. 20/40) orworse. For such eyes, there may be benefits by improving vision,including improving contrast at or near the limits of visual acuity ofthe amblyopic eye. Hence, exemplary aberration profiles may provideenhanced contrast, and/or enhanced RIQ (which may be eithermonochromatic RIQ, or polychromatic RIQ) at a range of spatialfrequencies according to the level of amblyopia of the eye. In someembodiments, the range of spatial frequencies for enhancement of RIQ maybe selected according to the application, such as the individualpatient's or eye's visual needs. For example, the range of spatialfrequencies may be 5 to 15 cycles/degree, 10 to 15 cycles/degree, 10 to20 cycles/degree, 15 to 20 cycles/degree, 15 to 25 cycles/degree, 20 to25 cycles/degree, 20 to 30 cycles/degree, or 25 to 30 cycles/degree, 25to 35 cycles/degree, 30 to 35 cycles/degree or 30 to 40 cycles/degree.

The fovea is the point on the retina that supports the most acutevision. In most normally-sighted eyes, the image of an object being‘looked at’ is located onto the fovea by rotation of the eye. Thisalignment of the visual object with the fovea is called “fixation”. Theability of the retina to resolve fine details decreases away from thefovea (central vision). Further out to the peripheral retina (peripheralvision), the visual acuity is progressively poorer. There are certaineyes that engage eccentric fixation. Eccentric fixation is the visionphenomenon when the eye does not use foveal vision. Such eyes, whenattempting to ‘look’ at an object, may place the image on some point inthe peripheral retina. The field angle range relative to the centralretina or fovea (which may be regarded as an optical axis of an eye, orof a model eye) that the image may be placed by the eccentric fixatingeye varies from eye to eye, but is typically consistent for the sameeye. This field angle range may be over a field angle of from on-axis(i.e. 0°) to the optical axis of the eye to 5° from the optical axis ofthe eye, or from on-axis to 10° from the optical axis of the eye. Ineyes with greater amounts of eccentric fixation, this field angle rangemay be over a field angle of from 5° from the optical axis of the eye to15° from the optical axis of the eye; or the field angle range may beover a field angle of from 10° from the optical axis of the eye to 20°from the optical axis of the eye Certain embodiments are directed toaberration profiles that provide a global RIQ (GRIQ) in which the rangeof field angles over which the GRIQ is effected need not include thecentral, on-axis or foveal visual point. Certain embodiments aredirected to aberration profiles that increase contrast from slightlylower than or near to the peripheral visual acuity of an eye or an eyewith conventional optical devices within a region of peripheral oreccentric viewing, to near to or slightly higher than the peripheralvisual acuity of an eye or an eye with conventional optical deviceswithin a region of peripheral or eccentric viewing. For example, theperipheral visual acuity of an eye with some embodiments may be 20/80(i.e. 6/24) or better at 20 degree field angle.

Candidate eye when defocus is corrected Candidate eye with and HOA isleft Defocus = −1 D uncorrected Pupil 6 6 SF-min 0 0 SF-max 60  60C(2,−2) 0 0 C(2,0) 1.29E+00 0 C(2,2) 0 0 C(3,−1) 0 −0.075 C(3,−1) 00.075 C(4,−2) 0 0.05 C(4,0) 0 0.3 C(4,2) 0 −0.05 C(5,−1) 0 0 C(5,1) 0 0C(6,−2) 0 −0.025 C(6,0) 0 0 C(6,2) 0 0.025 C(8,0) 0 0 C(10,0) 0 0C(12,0) 0 0 C(14,0) 0 0 C(16,0) 0 0 C(18,0) 0 0 C(20,0) 0 0Table 12.1 shows the aberration profiles for a) the candidate eye with−1 D; and b) when the defocus term of the candidate eye is corrected andhigher order aberrations are left uncorrected. The optical performanceof these two combinations in terms of the real part of the opticaltransfer function as a function of spatial frequencies are provided inFIGS. 134, 135 and 136.

In one other application, an eccentrically fixating eye may have abest-corrected peripheral visual acuity (i.e. the best visual acuityachievable using the best correction using conventional optical devicesfor its refractive error, which may be myopia or hyperopia orastigmatism or some combinations thereof, and for which visual acuity ismeasured at the eye's eccentric fixation visual point) of 6/18 (or20/60) acuity. This eccentric fixating, peripheral visual acuity levelmay be equated to a spatial frequency of 10 cycles per degree. In someexemplary embodiments, the combination of the higher aberration profilesprovides an enhanced (higher) contrast retinal image at the spatialfrequency range of 10 cycles per degree to 20 cycles per degree, as seenin combination #2 in FIG. 135; that is, from slightly lower than or nearto the peripheral visual acuity of the measured best-corrected(peripheral) visual acuity of the exemplary eccentric fixating eye, tonear to or slightly higher than the measured best-corrected visualacuity of the measured best-corrected visual acuity of the exemplaryeccentric fixating eye.

In other applications, the range of angles of eccentric fixation mayvary between 5° from the optical axis of the eye to 15° from the opticalaxis of the eye. In another embodiment, the combination of the higheraberration profiles provides an enhanced (higher) contrast retinal imageat the spatial frequency range of 20 cycles per degree to 30 cycles perdegree, as seen in combination #3 in FIG. 136. The aberration profilesof the exemplary higher order aberration combination improved contrastthat may translates to an increase in GRIQ for the exemplary eye withina field angle range selected to match the range of angle of eccentricfixation. When the optimised higher order aberration combinations areconfigured to the exemplary eye such that they increase the contrast atcertain ranges of spatial frequencies and field angles that have beenselected to substantially match the range of angles of eccentricfixation, the exemplary eye may achieve better vision performance andimproved contrast for a range of eccentric fixation.

Combination # 1 Combination # 2 Combination # 3 Pupil 6 6 6 SF-min 5 1025 SF-max 60 20 35 C(2,−2) 1.18E−10 −1.30E−08 2.29E−09 C(2,0) 0 0 0C(2,2) 2.42E−04 −2.25E−03 −1.14E−03 C(3,−1) −2.11E−09 −3.54E−09 4.46E−09C(3,−1) −1.95E−09 −2.25E−08 4.43E−09 C(4,−2) −8.62E−10 1.15E−10 8.58E−10C(4,0) 4.42E−02 −7.83E−03 −1.24E−02 C(4,2) −8.78E−04 −2.56E−03 1.02E−04C(5,−1) −1.97E−09 4.03E−09 −4.44E−08 C(5,1) −2.04E−09 1.43E−08 −4.46E−08C(6,−2) −4.17E−10 −7.37E−09 2.06E−08 C(6,0) −7.70E−02 −1.41E−01−5.85E−02 C(6,2) 4.46E−04 3.71E−03 −1.57E−04 C(8,0) −2.61E−03 7.00E−022.50E−02 C(10,0) −7.61E−02 −3.09E−02 −3.50E−02 C(12,0) 1.13E−01−4.01E−02 −4.08E−02 C(14,0) 1.25E−01 2.28E−02 −4.27E−02 C(16,0)−1.05E−01 −1.47E−02 5.21E−02 C(18,0) −9.37E−02 −3.06E−03 5.53E−02C(20,0) 1.84E−02 2.69E−02 −1.60E−02Table 12.2 shows the optimised aberration profiles that providesimprovement in the real part of the optical transfer function atselected spatial frequencies (observed in FIGS. 134, 135 and 136), whencompared with optical performance obtained with the two aberrationcombinations provided in Table 12.1.

Section 14: Implementation

There are several methods that may be used for designing or modellingthe lenses and/or devices disclosed herein. One exemplary method fordesigning one or more optical devices comprises: (a) setting a group oftarget requirements and a group of performance requirements for the oneor more optical devices that comprises two or more of the following: afocal distance, an optic zone, an image quality at the focal distance, athrough-focus image quality about the focal distance; wherein the imagequality is one of the following: monochromatic, polychromatic or globalimage quality; wherein the image quality is calculated in a spatialdomain or a Fourier domain, the image quality is calculated for at leasta portion of the optic zone diameter between 3 mm to 8 mm and for one ofthe following spatial frequency ranges: 0 to 15 c/d, 0 to 20 c/d, 0 to25 c/d, 0 to 30 c/d, 0 to 45 c/d, 0 to 60 c/d, 5 to 30 c/d or 0 to 60c/d; wherein the image quality is calculated by using one of thefollowing: tray-tracing, Fourier optics or direct wavefront propagation;(b) defining a wavefront representation of the one or more opticaldevices; wherein the wavefront representation optionally comprises oneof the following: apodisation, no apodisation, inverse apodisation orStiles-Crawford effect as apodisation; wherein the wavefrontrepresentation is described using one or more of the followingmathematical descriptions: Zernike polynomials, Fourier series, extendedeven or odd polynomials, extended aspheres, super conics and Besselseries; (c) optimising the represented wavefront in order tosubstantially achieve the target requirements of the performance of theone or more optical devices by using non-linear optimisation computationroutines. In some other exemplary methods, the optimisation of therepresented wavefront may be performed to achieve the performancerequirement at least one particular distance. In yet another exemplarymethod, the optimisation of the represented wavefront may be performedachieve the performance requirement at least two particular distances.

In yet another exemplary method, the optimisation of the representedwavefront may be performed achieve the performance requirement at leastthree particular distances. In yet another exemplary method, theoptimisation of the represented wavefront may be performed achieve theperformance requirement at least four particular distances. In yetanother exemplary method, the particular distances optimised for may bespaced apart by at least 0.5D. In yet another exemplary method, theparticular distances optimised for may be spaced apart by at least 1D.

In yet another exemplary method, the optimisation of the representedwavefront may be performed to have a negative or positive slope ofthrough-focus image quality in the negative or positive end of thethrough-focus range. Other suitable methods for designing and/ormodelling the lenses and/or devices disclosed herein may also be used.

Aberration profiles of the types described herein may be implemented ina number of lenses, ocular devices and/or methods. For example, contactlenses (hard or soft), corneal onlays, corneal inlays, and lenses forintraocular devices (both anterior and posterior chamber) may includethe combination aberration profiles discussed. Techniques to designlenses and to achieve a power profile are known and will are notdescribed herein in any detail. The aberration profiles can be appliedto spectacle lenses. However, because the aberration profiles requirealignment of the eye with the centre of the optics providing theaberration profile, then benefit may only be apparent for one particulardirection of gaze. Recently electro-active lenses have been proposedthat can track the direction of gaze and change the refractiveproperties of the lenses in response. Using electro-active lenses theaberration profile can move with the eye, which may increase the utilityof the disclosed aberration profiles for spectacle lenses.

The aberration profile may be provided on a lens which is an intraocularlens. In some embodiments, the intraocular lens may include haptics thatprovide for accommodation. In other embodiments, the lens may have afixed focal length. The aberration profile may be provided on asupplementary endo-capsular lens.

In certain applications, one or more of the disclosed aberrationprofiles may be provided to an eye through computer-assisted surgeryand/or methods of altering the power and/or aberration profile of theeye. For example implant, laser sculpting, laser ablation,thermokeratoplasty, lens sculpting are used for such a purpose. Examplesof such methods include radial keratotomy (RK), photorefractivekeratotomy (PRK), thermokeratoplasty, conductive keratoplasty, laserassisted in-situ keratomileusis (LASIK), laser assisted in-situepi-keratomileusis (LASEK) and/or clear lens extraction. For examplerefractive surgery or corneal ablation may be used to form a selectedaberration profile. The desired power profile or the desired change incorneal shape and/or power is substantially determined, or determined,and input to the laser system for application to the eye of the patient.Procedures may also be used to input a desired profile and/or aberrationprofile to the crystalline lens itself either by implant, laser ablationand/or laser sculpting to achieve a desired outcome. This includes, butnot limited to, systems that currently exist, including wavefront guidedfemto-second lasers.

Where the aberration profiles are to be included in a lens, then theaberration profile may first be translated into a lens thickness profilefor input to computer assisted manufacturing. Taking for example, thelens power profile D1 shown in FIG. 69, which is a combination ofZernike higher order spherical aberration terms, is converted to anaxial thickness, or a surface, profile for a contact lens, takingaccount of the refractive index of the contact lens material (in thiscase, contact lens material refractive index of 1.42). An examplethickness profile is shown in FIG. 70. In certain embodiments, featuresof the power or thickness profiles can either be put on the front or theback surface or a combination of both, under consideration of therefractive indices of lens and cornea. Once one or more of the followingparameters, i.e., the thickness profile, power profile, back surfaceshape, diameter and refractive index of the material have beendetermined, one or more of the parameters are input to a computerassisted lathe, or other manufacturing systems to produce the contactlens. Similar approaches can be adopted for other lenses and opticalsystems such as intra-ocular lenses, anterior and/or posterior chamberlenses, corneal implants, refractive surgery or combinations thereof.

The aberration profile may be selected and identified as a custom lensfor an individual. The process for design of the aberration profile mayinclude measuring the wavefront aberration of the eye and designing anaberration profile to achieve a through focus RIQ profile describedherein. The design process includes identifying the spherical aberrationin the natural eye and designing an aberration profile for the lens,device and/or method that, in combination with the spherical aberrationof the eye provides a required, or desired, RIQ profile. As describedherein, the required, or desired, RIQ profile may differ depending onthe application of the lens—as different requirements may apply between,for example, a person with progressing myopia and a person withpresbyopia. In some embodiments, other aberrations in the eye, forexample astigmatism, coma or trefoil are ignored.

In other embodiments, these are taken into account. For example, asdescribed herein, the presence of astigmatism affects the combinationsof aberrations that provide a through focus RIQ that inhibits eye growthunder the optical feedback explanation of emmetropisation. In otherembodiments, these aberrations are incorporated into the design. Forexample, when producing a lens design, a base lens may be produced thatcorrects for defocus and corrects one or more of astigmatism, coma andtrefoil. On top of this base profile is provided a spherical aberrationprofile designed to achieve (in the sense of using as an objectivedesign) the profiles described herein. The spherical aberration profilemay be selected using a trial and error, or iterative-convergenceapproach, for example by identifying a candidate profile, computing thethrough focus RIQ and evaluating whether the through focus RIQ has anacceptable profile. In another approach aberration profiles may bedesigned for population average, mean, median or other statisticalrepresentations or metrics. One approach for designing populationaverage, mean, median or other statistical representations or metrics,lenses is to normalise, or customise, or tailor, or optimise, the designfor a pupil size.

In certain embodiments, the description of the aberration profiles,first derivatives of the power profiles, second derivatives of the powerprofiles, Fourier transformation of the power profiles, power profilesand image profiles of the power profiles and/or other suitable orappropriate measures of one or more optical characteristics or one ormore performance metrics for lenses, devices and/or methods has beenprovided to some extent by way of mathematical explanation orderivation. This allows to some extent for precision in deriving and/ordescribing the aberration profiles, first derivatives of the powerprofiles, second derivatives of the power profiles, Fouriertransformation of the power profiles, power profiles and image profilesof the power profiles for lenses.

However, in certain applications, lenses, devices and/or methods may ormay not have precision that is comparable to, or commensurate with orderived from the mathematical calculations. For example tolerances andinaccuracies arising during manufacture may or may not result invariations of the lens profile. In certain embodiments, the powerprofile and/or aberration profile of a lens may be approximatelymeasured using, for example, a wavefront aberrometer. From this anapproximate measure of through focus RIQ may be determined; for example,using visual Strehl Ratio. In certain embodiments, the power profileand/or aberration profile of a lens may be characterised by using, forexample, suitable instruments and/or techniques such as Hartman-Shackaberrometry, ray-tracing, lens power mapping, focimetry, interferometry,phase contrast, ptchyography, Foucault knife-edge systems, orcombinations thereof. From these characterisations one or more of thefollowing: aberration profiles, first derivatives of the power profiles,second derivatives of the power profiles, Fourier transformation of thepower profiles, power profiles and image profiles of the power profilesand/or other suitable or appropriate measures of one or more opticalcharacteristics or one or more performance metrics, may be measured,derived or otherwise determined.

Aberration profiles may be implemented in a number of lenses, devicesand/or methods, according to certain embodiments. For example, the lensmay be characterised by testing the lens on a ray tracing or physicalmodel eye with a focal length equal to, or substantially equal to, thefocal distance of the lens. The aberration profile of the lens,including higher order aberration profiles, that would result in animage on the retina which may be quantified using one or more of the RIQmetrics disclosed. In certain embodiments, the model eye may have no, orsubstantially no, aberrations. In certain embodiments, the RIQ metricmay be visual Strehl ratio. In other embodiments, the pupil size may beselected from one or more of the following ranges: 2 to 8 mm, 2 to 7 mm,2 to 6 mm, 3 to 6 mm, 3 to 5 mm, 4 to 6 mm or 5 to 7 mm. In some otherembodiments, the spatial frequency ranges can be selected from one ofthe following: 0 to 30 cycles/degree, 0 to 60 cycles/degree or 0 to 45cycles/degree. In other embodiments, the selected wavelength forcalculations of one or more RIQ metrics may be selected from one or moreof the following: 540 nm to 590 nm inclusive, 420 nm to 760 nminclusive, 500 nm to 720 nm inclusive or 420 nm to 590 nm inclusive. Incertain embodiments, the RIQ may be measured on an on-axis model eye. Inother applications an off-axis model eye may be used to obtain other RIQvariants like the global RIQ. The through-focus RIQ may be calculated onthe model eye by using spherical lenses in front the model eye.

Certain embodiments disclosed herein are directed to methods ofcorrecting vision whereby a lens of one or more of the disclosedembodiments is prescribed according to one or more target refractivepowers, an appropriate power profile, and the lens is fitted to an eyeto provide a visual performance for the eye, along a range ofsubstantially continuous visual distances, including intermediate andfar distances, wherein the visual performance of the lens is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance.

Certain embodiments disclosed herein are directed to methods ofcorrecting vision whereby a lens of one or more of the disclosedembodiments is prescribed according to one or more target refractivepowers, an appropriate power profile, and the lens is fitted to an eyeto improve the visual performance for the eye. In certain applications,one or more methods disclosed herein may be used for correcting visionof the eye according to certain embodiments, whereby the eye is affectedby one or more of the following: myopia, hyperopia, emmetropia,astigmatism, presbyopia and optically aberrated.

Certain embodiments, may be used in methods for correcting the vision ofa pair of eyes, whereby one or both of the eyes is optically aberratedpossesses at least one higher-order aberration. Certain embodiments, maybe used in methods of correcting binocular vision, whereby two lenses ofone or more embodiments disclosed herein are prescribed according to afirst and a second target refractive power, a first and a second powerprofile are selected, and the two lenses fitted to a pair of eyesimprove the visual performance of the two eyes combined compared toindividual eyes separately. In certain methods disclosed herein, thefirst target refractive power is different from the second targetrefractive power.

Certain embodiments are directed to methods of correcting binocularvision, whereby the first target refractive power is selected to improvevisual performance at a visual distance that is at least one of thefollowing: far, intermediate, near; and the second target refractivepower is selected to improve visual performance at a visual distancethat is at least one of the following: far, intermediate, near; whereinthe visual distance at which the visual performance for which the firsttarget refractive power is selected is different from the visualdistance at which the visual performance for which the second targetrefractive power is selected. In certain applications, one or moremethods disclosed herein may be used for correcting vision of the eyeaccording to certain embodiments, whereby the refractive state of theeye may be classified as one or more of the following: myopia,hyperopia, emmetropia, regular astigmatism, irregular astigmatism,optically aberrated, presbyopia, non-presbyopia.

Certain embodiments are directed to methods of manufacturing lenseswhere the lenses are configured or designed according to a referenceeye, whereby the lens features that are configured are selected from oneor more of the following: focal length, refractive power, power profile,number of spherical aberration terms, magnitude of spherical aberrationterms; whereby the reference eye is selected from one or more of thefollowing: an individual eye, both eyes of an individual person,statistical representation of eyes a sample of an affected population,computational model of an eye and/or computational model of eyes of anaffected population.

In certain embodiments, aperture size may be used to characterise anentrance pupil of the eye and/or a portion of the optic zone of a lensand/or device. In certain applications, the effective aperture sizemaybe defined as an opening that is greater than or equal to 1.5 mm, 2mm, 3 mm, 4 mm, 5 mm, 6 mm or 7 mm, this is in contrast to pin-holeapertures which typically have a diameter, for example, less than 1.5mm. For example, certain embodiments are directed to a lens comprising:an optical axis; at least two optical surfaces; wherein the lens isconfigured to provide a visual performance on a presbyopic eyesubstantially equivalent to the visual performance of a single-visionlens on the pre-presbyopic eye; and wherein the lens has an aperturesize greater than 1.5 mm.

Certain embodiments are directed to one or more methods of surgicalcorrection of vision to improve visual performance. For example, amethod for surgical correction may comprise the steps of: (1) computingone or more targeted modifications to the optical properties, powerand/or physical structure of an eye; wherein the targeted modificationscomprise: at least one desired refractive power and at least oneappropriate power profile; at least one aberration profile, wherein theaberration profile is comprised of at least two spherical aberrationterm and a defocus term; and a visual performance along substantiallycontinuous visual distances including near, intermediate and far,wherein the visual performance of the eye along the substantiallycontinuous visual distance is substantially equivalent to the visualperformance of an eye wearing an correctly prescribed single-vision lensfor the far visual distance; (2) inputting the desired modifications toan ophthalmic surgical system; and (3) applying the desiredmodifications to the eye with the ophthalmic surgical system. In certainapplications, the visual performance of the eye is further characterisedby minimal, or no, ghosting at near, intermediate and far visualdistances.

In certain applications, the vision performance of the correctlyprescribed single vision lens provides a visual acuity for the eye thatis the best-corrected visual acuity. In certain applications, thebest-corrected visual acuity is a visual acuity that cannot besubstantially improved by further manipulating the power of thecorrectly prescribed single vision lens. In certain applications, theaberration profile comprises three or more spherical aberration termsand a defocus term.

Certain embodiments are directed to lenses that provide substantiallyequivalent, or equivalent or better optical and/or visual performancethan a correctly prescribed single vision lens at far visual distance.As used in certain embodiments, correctly prescribed may mean aprescribed single vision lens at the far visual distance that provides avisual acuity for an eye that is the best-corrected visual acuity andcannot be substantially improved by further manipulating or adjustingthe power of the lens. As used in certain embodiments, appropriately,properly, effectively, prescribed may mean a prescribed single visionlens at the far visual distance that provides a visual acuity for an eyethat approximates the best-corrected visual acuity and cannot besubstantially improved by further manipulating or adjusting the power ofthe lens.

Certain embodiments are directed to one or more methods of surgicalcorrection of vision to improve visual performance. For example, amethod of correcting vision comprising the steps of: (1) computing oneor more targeted modifications to an eye; wherein the modificationsprovides to the eye: at least one optical characteristic; wherein the atleast one optical characteristic comprises at least one aberrationprofile; the aberration profile comprises at least two sphericalaberration term and a defocus term; and a visual performance atintermediate and far visual distances that is at least substantiallyequivalent to the eye fitted with an correctly prescribed single-visionlens for far visual distance; wherein when tested with a defined visualrating scale of 1 to 10 units, the visual performance of the eye at thenear visual distance is within two units of the visual performance ofthe eye fitted with an correctly prescribed single-vision lens at fardistance; (2) inputting the desired modifications to an ophthalmicsurgical system; and (3) applying the targeted modifications to the eyewith the ophthalmic surgical system. In certain applications, the visualperformance additionally provides substantially minimal ghosting to thevision of the eye at near, intermediate and far visual distances. Incertain applications, the substantially equivalent to or better visualperformance is determined at least in part by a visual rating scale of 1to 10 units.

Certain embodiments are directed to one or more methods of surgicalcorrection of vision to improve visual performance. For example, methodsof vision correction may comprise the steps of: (1) computing one ormore targeted modifications to an eye; wherein the modifications provideto the eye: at least one optical characteristic; wherein the at leastone optical characteristic comprises at least one aberration profile;the aberration profile comprises at least two spherical aberration termand a defocus term; and a visual performance at intermediate and farvisual distances, that is substantially equivalent to, or better than,the eye fitted with a correctly prescribed single-vision lens for farvisual distance; and wherein the visual performance is furthercharacterised by minimal ghosting to the vision of the eye at least atfar distance; (2) inputting the desired modifications to an ophthalmicsurgical system; and (3) applying the desired modifications to the eyewith the ophthalmic surgical system. In certain applications, theminimal ghosting is attaining a score of less than or equal to 2.4, 2.2,2, 1.8, 1.6 or 1.4 on the vision rating ghosting scale of 1 to 10 units.

Certain embodiments are directed to one or more devices and/or systemsfor the surgical correction of vision to improve visual performance. Forexample, a device and/or system for correcting vision of an eye maycomprise: (1) an input module; (2) a computation module; and (3) adelivery module; wherein the input module is configured to receive inputrelevant to the vision correction of the eye; the computation module isconfigured to compute one or more targeted modifications to the eye;wherein the modifications provides to the eye: at least one targetedrefractive power and at least one appropriate power profile; at leastone aberration profile, wherein the aberration profile being comprisedof at least two spherical aberration term and a defocus term; and avisual performance, along substantially continuous visual distances,including intermediate and far, wherein the visual performance of theeye along the substantially continuous visual distance is substantiallyequivalent to the visual performance of an eye wearing an correctlyprescribed single-vision lens for the far visual distance; and thedelivery module uses the computed targeted modifications to the eyecomputed by the computation module to deliver the targeted modificationsto the eye. In certain applications, the visual performance of the eyeis further characterised by minimal, or no, ghosting at near,intermediate and far visual distances.

In certain applications, the correctly prescribed single vision lensprovides a visual acuity for the eye that is the best-corrected visualacuity. In certain applications, the best-corrected visual acuity is avisual acuity that cannot be substantially improved by furthermanipulating the power of the correctly prescribed single vision lens.In certain applications, the aberration profile comprises three or morespherical aberration term and a defocus term. In certain applications,the delivery module may be an ophthalmic refractive surgical system suchas a femto-second laser.

Certain embodiments are directed to one or more devices and/or systemsfor the surgical correction of vision to improve visual performance. Forexample, a device and/or system for correcting vision of an eye maycomprise: (1) an input module; (2) a computation module; and (3) adelivery module; wherein the input module is configured to receive inputrelevant to the vision correction of the eye; the computation module isconfigured to compute one or more desired modifications to the eye;wherein the modifications provides to the eye: at least one opticalcharacteristic; wherein the at least one optical characteristiccomprises at least one aberration profile; the aberration profilecomprises at least two spherical aberration term and a defocus term; anda visual performance at intermediate and far visual distances that issubstantially equivalent to or better than the eye fitted with ancorrectly prescribed single-vision lens for far visual distance; andwhen tested with a defined visual rating scale of 1 to 10 units, thevisual performance of the eye at the near visual distance is within twounits of the visual performance of the eye fitted with an correctlyprescribed single-vision lens at far distance; the delivery moduleutilising desired modifications to the eye computed by the computationmodule to deliver the desired modifications to the eye.

In certain applications, the visual performance in addition, providesminimal ghosting to the vision of the eye at near, intermediate and farvisual distances. In certain applications, the substantially equivalentto or better visual performance is substantially determined at least inpart by a visual rating scale of 1 to 10 units. In certain applications,the delivery module is an ophthalmic refractive surgical system such asa femto-second laser.

Certain embodiments are directed to one or more devices and/or systemsfor the surgical correction of vision to improve visual performance. Forexample, a device and/or system for correcting vision of an eye maycomprise: (1) an input module; (2) a computation module; and (3) adelivery module; wherein the input module is configured to receive inputrelevant to the vision correction of the eye; wherein the computationmodule is configured to compute one or more targeted modifications tothe eye; wherein the modifications provides to the eye: at least oneoptical characteristic; wherein the at least one optical characteristiccomprises at least one aberration profile; wherein the aberrationprofile comprises at least two spherical aberration terms and a defocusterm; and a visual performance at intermediate and far visual distances,that is substantially equivalent to, or better than, the eye fitted witha correctly prescribed single-vision lens for far visual distance; andwherein the visual performance is characterised by minimal ghosting tothe vision of the eye at least at far distance; and the delivery moduleutilising the computed targeted modifications to the eye computed by thecomputation module to deliver the desired modifications to the eye.

In certain applications, the minimal ghosting has a score of less thanor equal to 2.4, 2.2, 2, 1.8, 1.6 or 1.4 on the vision rating ghostingscale of 1 to 10 units. In certain applications, the delivery module isan ophthalmic refractive surgical system such as a femto-second laser.

In certain embodiments, the lens is configured to provide visionsubstantially equivalent, or better, to distance vision corrected with acorrectly prescribed lens for the refractive error for distance across adioptric range of 0D to 2.5D or from infinity to 40 cm with minimalghosting for emmetropes, myopes, hyperopes and astigmats.

In certain applications, the lenses substantially correct the distancerefractive error; wherein the lens is configured to enable myopia to beslowed without the loss of vision as is usually associated withmultifocal contact lenses and provides excellent vision across thevisual field for example, 30 degrees nasal to 30 degrees temporal andalso allows the provision of lenses that give retinal image quality of0.4 or above for either a chosen focal distance or averaged across focaldistances from infinity to 40 cm with an average of 0.3 retinal imagequality. Such lenses when optimising retinal image quality provideexceptionally clear high contrast images at the chosen distances;wherein the lens provides exceptional image quality and visualperformance with minimal ghosting across the range of dioptric distancesfrom infinity to near for the correction of refractive errors andtreatment of presbyopia and myopia control; when tested with a definedoverall visual rating scale of 1 to 10 units, the multifocal lens isconfigured such that the overall visual performance of the multifocallens is substantially equivalent to or better than an correctlyprescribed single-vision lens for far visual distance.

In certain embodiments, the visual performance of a candidate eye, alonga range of substantially continuous visual distances, including near,intermediate and far distances, wherein the visual performance of themultifocal lens is at least substantially equivalent to the visualperformance of a correctly prescribed single-vision lens at the farvisual distance.

In certain embodiments, the term minimal ghosting may mean a lack of anundesired secondary image appearing at the image plane of the opticalsystem. In certain embodiments, the term minimal ghosting may be used torepresent an undesired secondary image appearing on the retina of theeye. Conversely, the term lack of ghosting may represent an undesireddouble image appearing on the retina of the eye. In certain embodiments,minimal ghosting may represent a lack of an undesired double imageperceived by the candidate eye. In other applications, minimal ghostingrepresents a lack of false out-of-focus image appearing along side ofthe primary image in an optical system.

Section 14.A: Asymmetric HOA and Image Quality

In certain embodiments, the choice of higher order aberrations beingoptimised for a desired through-focus image quality may includeasymmetric higher order aberrations from one or more of the following:primary horizontal astigmatism, primary vertical astigmatism, secondaryhorizontal astigmatism, primary horizontal coma, primary vertical coma,secondary primary horizontal coma, secondary vertical coma, etc inaddition to the rotationally symmetric higher order aberrationsdisclosed herein. In some other embodiments, the choice of asymmetrichigher order aberrations may also include tertiary, quaternary,pentanary, hexanary, octanary, nanonary asymmetric higher orderaberrations. For example, the Zernike coefficients represented byC(3,−1), C(3,1), C(5,−1), C(5,1), C(7,−1), C(7,1), C(9,−1), C(9,1),C(11,−1), C(11,1), (8,−2), (8,2), (10,−2), (10,2), (12,−2), (12,2),(14,−2), (14,2), etc.

Domain) Domain) Spatial Frequency 0 to 20 0 to 25 0 to 25 0 to 25cyc/deg cyc/deg cyc/deg cyc/deg Pupil 4 3 3 4 Zernike C(2,−2) 0.1220.150 0.000 0.000 coefficients C(2,0) 0 0 0 0 C(2,2) −0.002 0.150 0.000−0.168 C(3,−1) 0 0 0 0 C(3,−1) 0 0 0 0 C(4,−2) 0.113 −0.054 0.000 0.000C(4,0) −0.200 −0.150 −0.076 −0.200 C(4,2) 0.002 0.051 0.000 −0.089C(5,−1) 0 0 0 0 C(5,1) 0 0 0 0 C(6,−2) 0.050 0.010 0.000 0.000 C(6,0)−0.133 −0.140 −0.150 −0.079 C(6,2) 0.000 −0.006 0.000 0.049 C(8,0)−0.148 −0.091 0.018 0.040 C(10,0) −0.053 −0.055 −0.099 0.075 C(12,0)0.010 −0.009 −0.069 0.054 C(14,0) −0.051 0.014 −0.052 0.000 C(16,0)−0.086 0.032 −0.044 −0.034 C(18,0) −0.050 0.027 −0.004 −0.037 C(20,0)−0.014 0.020 −0.040 −0.018Table 12.4 shows the optimised higher order aberration combinationsincluding both symmetric and asymmetric higher order aberrations (IC-1to IC-4 that provides a through focus image quality described in theFIG. 132.

For example, the optimised higher order aberration combinations IC-1 toIC-8 shown in the table 12.4 are configured to provide the through focusimage quality shown in the FIG. 132. The computations discussed in thissection are performed for pupil diameter of 3 mm and 4 mm and using thesimple Strehl ratio and visual Strehl ratio in frequency domain as imagequality metrics. In other embodiments, computations with other pupildiameters ranging from 3 to 8 mm and utilising other image qualitymetrics described in the section 1 may also be used.

Design combination IC-5 IC-6 IC-7 IC-8 Image Quality metric VisualStrehl Visual Strehl with PTF Simple Strehl Simple Strehl with PTF(Frequency (Frequency (Frequency (Frequency Domain) Domain) Domain)Domain) Spatial Frequency 0 to 30 cyc/deg 0 to 30 cyc/deg 0 to 20cyc/deg 0 to 30 cyc/deg Pupil 3 3 3 4 Zernike C(2,−2) 0.000 0.000 0.000−0.200 coefficients C(2,0) 0 0 0 0 C(2,2) 0.000 0.000 0.063 −0.181C(3,−1) 0 0 0 0 C(3,−1) 0 0 0 0 C(4,−2) 0.000 0.000 0.000 0.053 C(4,0)−0.103 −0.012 −0.051 −0.200 C(4,2) 0.000 0.000 −0.060 −0.056 C(5,−1) 0 00 0 C(5,1) 0 0 0 0 C(6,−2) 0 0 0 −0.038 C(6,0) 0 0.083 −0.010 −0.162C(6,2) 0 0 −0.026 0.037 C(8,0) −0.002 −0.001 −0.064 −0.037 C(10,0)−0.014 −0.023 −0.020 0.027 C(12,0) 0.020 0.017 0.061 0.092 C(14,0) 0.0420.001 0.062 0.087 C(16,0) 0.016 −0.020 0.038 0.073 C(18,0) −0.018 0.0070.043 0.035 C(20,0) −0.019 0.020 0.033 0.014Table 12.5 shows the optimised higher order aberration combinationsincluding both symmetric and asymmetric higher order aberrations (IC-5to IC-8 that provide a through focus image quality described in the FIG.132

Section 14.B: Decentred and/or Non Co-Axial

The eye comprises various components and surfaces that combine toproduce the optical characteristics of the eye. In lens design, it issometimes useful to assume the eye, its components and associatedsurfaces are co-axial. There are, however, other cases when thecomponents and associated surfaces of the eye may not be assumed to beco-axial. For example, the axis of the cornea may not be aligned withthe centre of the pupil. Non-alignment of axes may be a translationand/or a tilt. Combinations of translation and tilt misalignment mayalso occur. When two or more landmarks (e.g. axes, centre, etc) aremutually or relatively misaligned (i.e. not co-axial or “spaced-apart”),the eye, or eye and lens combination, is not symmetrical. The directionof misalignment may be superiorly (or upwards), or inferiorly (ordownwards), or nasally (in the direction across the eye towards the noseof the patient), or temporally (in the direction across the eye towardsthe nearer ear of the patient), or one or more combinations of thosedirections.

In certain embodiments, a lens may comprise an optic zone that may becircular, elliptical, non-circular, non-elliptical or combinationsthereof. For example, a contact lens. The optic zone may also berotationally asymmetrical and/or laterally (mirror-image) asymmetrical.With respect to optical performance and/or visual performance, an opticzone may have an optical axis, the optical axis being associated withthe optical performance and/or visual performance provided by theaberration profile of the types described herein.

In some embodiments, the centre, geometrical centre or centroid(defined, for example, as a standard mathematical, geometry definitionfor the centroid of a shape) of the optic zone may be spaced-apart (i.e.not co-located) from its optical axis. Such embodiments may bebeneficial for the delivery of desired optical performance and/or visualperformance to eyes that exhibit, at least in part, non-co-axialalignment of its components and/or associated surfaces. For example, thepupil area may be, at least in part, non-circular and at least in part,decentred/misaligned relative to the cornea of an eye. A contact lensfor such an exemplary embodiment may be beneficial to the opticalperformance and/or visual performance, if the optic zone is decentredwhile the optic axis of the contact lens remains substantially alignedwith the optical axis of the eye. The amount that the centroid of theoptic zone and the optical axis of the contact lens may be space-apartmay be selected according to an individual eye, a population average, arepresentative value for a sub-population or combinations thereof, andmay be at least 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm or 1 mm.In some embodiments, the amount of spacing-apart may be between 0.1 mmto 0.5 mm, 0.5 mm to 1 mm, 1 mm to 1.5 mm, 1.5 mm to 2 mm or 2 mm to 3mm.

With respect to decentred and non-coaxial lenses, a lens may comprise anoptic zone and a carrier. The optic zone is a region, or regions, of alens that provides the desired optical performance including, forexample, aberration profiles of the types described herein. The carrierof a lens is a region, or regions, of a lens that is not intended toprovide the optical performance but may be configured to control theinteraction of the lens with the eye. For example, a contact lens.

In some embodiments, a carrier may have surface blending, thickness andthickness profiles, edge profiles, etc, to deliver a level of comfort tothe contact lens wearer. In other embodiments, a carrier may beconfigured to control the lateral position or/and rotational orientationof the lens. Such carrier configurations may locate a lens in aparticular orientation, or a particular range of orientation, and may bebeneficial in lenses which possess an amount of asymmetry by ensuringsubstantial alignment of the lens when applied to the eye.Configurations may include prism ballast, lens edge truncation, dynamicthin-zones, slab-off, double slab-off, horizontal iso-thickness,corridor of thin-zones, etc. In such embodiments, a lens may comprise anoptic zone and a carrier in which the centroid of the optic zone isspaced-apart from the optical axis while the carrier may be configuredto control the orientation of the lens. The amount that the centroid ofthe optic zone and the optical axis of the lens may be space-apart maybe selected according to an individual eye, or a population average, ora representative value for a sub-population, and may be at least 0.1 mm,0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm or 1 mm. In some embodiments, theamount of spacing-apart may be between 0.1 mm to 0.5 mm, 0.5 mm to 1 mm,1 mm to 1.5 mm, 1.5 mm to 2 mm or 2 mm to 3 mm.

In certain embodiments, a lens may comprise an optic zone and a carrier,wherein the internal (nearer an optic zone), external (nearer theoutside edge of a lens), or both boundaries of the carrier may becircular, elliptical, non-circular, non-elliptical or combinationsthereof. In some embodiments, the carrier and/or the optic zone may havemultiple boundaries. The carrier may be rotationally asymmetrical and/orlaterally (e.g. mirror-image) asymmetrical. In such embodiments, thecentre, geometrical centre or centroid (defined, for example, as astandard mathematical, geometry definition for the centroid of a shape)of the carrier may be spaced-apart (i.e. not co-located) from theoptical axis associated with the optic zone of the contact lens, whilethe carrier may be configured to control the orientation of the contactlens. Such embodiments may be beneficial because they provide desiredoptical performance and/or visual performance to eyes that exhibit, atleast in part, non-co-axial alignment of its components and/orassociated surfaces. For example, for a contact lens applied to an eyeby placement over the cornea, the cornea may be, at least in part,asymmetrical and at least in part, misaligned/non-co-axial with theoptical axis of the eye. A contact lens for such exemplary cases may beconfigured such that the centroid of the carrier is decentred withrespect to the optical axis associated with the optic zone of thecontact lens. The amount that the optical axis and the centroid of thecarrier of the contact lens may be spaced-apart may be selectedaccording to an individual eye, a population average or a representativevalue for a sub-population, and may be at least 0.1 mm, 0.2 mm, 0.3 mm,0.4 mm, 0.5 mm, 0.7 mm or 1 mm. In some embodiments, the amount ofspacing-apart may be between 0.1 mm to 0.5 mm, 0.5 mm to 1 mm, 1 mm to1.5 mm, 1.5 mm to 2 mm, 2 mm to 3 mm or 3 mm to 4 mm.

In certain embodiments, a lens may be a contact lens that may comprisean optic zone and a carrier. The optic zone being a region, or regionsthat provides an optical performance including, for example, aberrationprofiles of the types described in this application. The carrier may berotationally asymmetrical and/or laterally (e.g. mirror-image)asymmetrical. In some embodiments, a carrier may have surface blending,thickness and thickness profiles, edge profiles, etc, to deliver a levelof comfort to the contact lens wearer. In other embodiments, a carriermay be configured to control the lateral position or/and rotationalorientation of a contact lens. Such carrier configurations may locate acontact lens in a particular orientation, or a particular range oforientations. Configurations may include prism ballast, lens edgetruncation, dynamic thin-zones, slab-off, double slab-off, horizontaliso-thickness, corridor of thin-zones, etc. For such embodiments, a lensmay be a contact lens that may comprise an optic zone and a carrier inwhich the centre, or geometrical centre, or centroid of the optic zonemay be spaced-apart (i.e. not co-located) from the centre, geometricalcentre or centroid of the carrier, while the carrier may be configuredto control the orientation of the contact lens. Such an arrangement maybe beneficial for the delivery of desired optical performance and/orvisual performance to eyes that exhibit non-co-axial alignment of itscomponents and/or associated surfaces. The amount that the centroid ofthe optic zone and the centroid of the carrier of the contact lens maybe spaced-apart may be selected according to an individual eye, apopulation average or a representative value for a sub-population, andmay be at least 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm or 1 mm.In some embodiments, the amount of spacing-apart may be between 0.1 mmto 0.5 mm, 0.5 mm to 1 mm, 1 mm to 1.5 mm, 1.5 mm to 2 mm or 2 mm to 3mm.

In certain embodiments, a lens may comprise an optic zone and a carrierin which the centroid of the optic zone, the optical axis and thecentre, the geometrical centre or the centroid of the carrier aremutually spaced-apart (i.e. not co-located) from each other, while thecarrier may be configured to control the orientation of the contactlens. Such an arrangement may be beneficial for the delivery of desiredoptical performance and/or visual performance to eyes that exhibitnon-co-axial alignment of its components and/or associated surfaces. Theamount that the optical axis associated with the optic zone, thecentroid of the optic zone, and the centroid of the carrier of thecontact lens may be mutually spaced-apart may be selected according toan individual eye, a population average or a representative value for asub-population, and may be at least 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5mm, 0.7 mm or 1 mm, and may be pair-wise different (i.e. the amount thatthe optical axis is spaced-apart from the centroid of the optic zone maydiffer from the amount that the optical axis is spaced-apart from thecentroid of the carrier, and either of the amounts may differ from theamount that the centroid of the optic zone is spaced-apart from thecentroid of the carrier. In some embodiments, the amount ofspacing-apart may be between 0.1 mm to 0.5 mm, 0.5 mm to 1 mm, 1 mm to1.5 mm, 1.5 mm to 2 mm or 2 mm to 3 mm.

Section 14.C: Effect of Prism

In some embodiments, the optical device may possess a limited amount ofoptical tilt or prismatic term in addition to the designed aberrationprofile. Typically it may be desirable to limit the amount of opticaltilt or prism terms such that it does not substantially interfere withvision. In some embodiments, tilt may be introduced intentionally, forexample, to help with the rotational stabilisation of toric contactlenses. In certain embodiments, tilt may be introduced unintentionally,for example, due to manufacturing limitations. Typically, the opticalperformance may be unaffected by tilt. For certain eye conditions,however, optical prism may have a beneficial and/or therapeutic effectby tilting the optical axis differently in one eye compared against itsfellow eye. In this case, a rotational stabilisation feature may beincluded into the design.

Section 14.D: Tear Film/Surface Treatment

Subjective vision ratings may be affected by the on-eye comfort of acontact lens and vice versa. Therefore, visual satisfaction may beenhanced by adding one or more features to a contact lens that providesan increase in perceived comfort. In order for contact lenses to providean acceptable fit and comfort on an eye, it may be desirable for thelens to be covered by a thin layer of tears on the anterior andposterior surface of the lens. Some embodiments may have one or moresurfaces that are treated in a way to manipulate the tear layer suchthat it contributes to the aberration profile. Certain materials and/ormanufacturing processes may be used to manipulate a tear layer. Suchmaterials or manufacturing process may be used with some of thedisclosed embodiments. One or more surface treatments may be used tomanipulate the tear layer of some embodiments. For example, surfacetreatment may include one or more of the following: plasma treatment,layer by layer surface coating, adding wetting agents to the packagingsolution or contact lenses, applying eye drops or combinations thereof.A contact lens with no pre-lens tear film may also provide consistentoptical performance, according to some embodiments.

Section 15: Exemplary Sets of Lens Designs which are SubstantiallyIndependent of Inherent Spherical Aberration of the Eye

The interactions between the inherent aberration profiles of thecandidate eyes and those of a selected combination of a design set mayhave a) an improved effect; b) degraded effect; or c) no substantialeffect on the objective and/or subjective optical and/or visualperformance.

The present disclosure provides embodiments directed to choosing betweena positive and/or negative phase of a particular combination ofaberration profile to be able to attain a specific goal for thecandidate eye. The specific goal for instance may be to change the slopeof through-focus RIQ in the direction that would favour theemmetropisation process for myopic or hyperopic eyes; or alternativelysimilar approach, or methods, may be used to mitigate the presbyopicsymptoms in alternative candidate eyes.

Certain embodiments are directed to a lens, device and/or method thatenables the designing of lenses which when applied to a candidate eyemay produce a visual performance that is substantially independent ofthe aberration profile of that candidate eye. Substantially independent,in certain applications, means that lenses may be designed that provideacceptable and/or similar performance on a plurality of candidate eyesthat are within the representative sample of the target populations. Incertain applications, methods to obtain a target TFRIQ include use of anon-linear, unconstrained optimization routine and one or more othervariables. The variables selected for the non-linear, unconstrained,optimisation routine may include a chosen group of Zernike sphericalaberration coefficients, from C (2, 0) to C (20, 0) and one or moreother variables. The other variables, for example, may be aberrationprofiles of a representative sample of the target population.

Lenses may be designed by selecting an optimisation routine to evaluatea through-focus RIQ may include: a) a target TFRIQ; b) a target TFRIQwithin predefined bounds; or c) combination of a) and b). Iteration G1(FIG. 71) is one exemplary of a lens design whose visual performance isindependent of the inherent aberration profile of the candidate eye.

Table 13 provides the defocus term and the rest of combinations ofspherical aberration terms, denoted in Zernike coefficients C(2,0) toC(20,0), that represents the exemplary design at 4, 5 and 6 mm opticzone or pupil diameter.

TABLE 13 Defocus and higher order spherical aberration coefficients, at4, 5 and 6 mm optic zone diameter, of an exemplary embodiment whoseperformance is substantially independent of the inherent sphericalaberration of the candidate eye for at least at 4 and 5 mm pupildiameters of the candidate eye. Iteration G1 At 4 mm At 5 mm At 6 mmC(2,0) 0.442 0.558 0.47 C(4,0) −0.103 −0.096 −0.241 C(6,0) −0.081 0.0380.038 C(8,0) 0.032 0.017 0.046 C(10,0) 0.056 −0.086 0.043 C(12,0) −0.017−0.027 0.057 C(14,0) −0.023 0.053 −0.056 C(16,0) 0.01 −0.005 −0.053C(18,0) 0.004 −0.017 0.051 C(20,0) −0.002 0.017 0.006

FIG. 72 shows a graph of the through focus performance of Iteration G1for a 4 mm pupil size, for a range of inherent spherical aberrationranging from −0.1 μm to +0.2 μm (and no other inherent aberrations).FIG. 73 shows the corresponding performance for a 5 mm pupil size. Forboth the through focus performance is relatively constant despitevariations in inherent spherical aberration. Accordingly, lenses ofIteration G1 lenses with aberration profiles of similar characteristicsmay be prescribed to a relatively large number of recipients in apopulation. The through focus performance of Iteration G1 for both 5 mmand 4 mm pupil sizes are shown in Tables 14, 15, 16 and 17 for inherentprimary spherical aberration of −0.10 μm, 0.00 μm, +0.10 μm and +0.20μm, respectively, all measured assuming a 5 mm pupil.

TABLE 14 The through focus performance of Iteration G1, for both 5 mmand 4 mm pupil sizes, on candidate eye with an inherent primaryspherical aberration C(4,0) of −0.10 μm of the candidate eye measured at5 mm pupil. Defocus 4 mm 5 mm −2.5 0.001 0.003 −2.25 0.001 0.004 −20.001 0.005 −1.75 0.002 0.007 −1.5 0.002 0.011 −1.25 0.002 0.018 −10.014 0.032 −0.75 0.065 0.060 −0.5 0.174 0.121 −0.25 0.293 0.217 0 0.3390.336 0.25 0.309 0.443 0.5 0.297 0.452 0.75 0.348 0.378 1 0.409 0.3221.25 0.428 0.305 1.5 0.378 0.291 1.75 0.270 0.249 2 0.164 0.182 2.250.096 0.115 2.5 0.057 0.067

TABLE 15 The through focus performance of Iteration G1, for both 5 mmand 4 mm pupil sizes, on candidate eye with an inherent primaryspherical aberration C(4,0) of 0.00 μm of the candidate eye measured at5 mm pupil. Defocus 4 mm 5 mm −2.5 0.002 0.004 −2.25 0.003 0.005 −20.003 0.005 −1.75 0.004 0.006 −1.5 0.005 0.008 −1.25 0.007 0.015 −10.011 0.030 −0.75 0.036 0.063 −0.5 0.115 0.131 −0.25 0.267 0.246 0 0.4240.361 0.25 0.464 0.436 0.5 0.398 0.492 0.75 0.368 0.488 1 0.398 0.4171.25 0.391 0.333 1.5 0.320 0.252 1.75 0.221 0.177 2 0.132 0.110 2.250.074 0.062 2.5 0.040 0.035

TABLE 16 The through focus performance of Iteration G1, for both 5 mmand 4 mm pupil sizes, on candidate eye with an inherent primaryspherical aberration C(4,0) of 0.10 μm of the candidate eye measured at5 mm pupil. Defocus 4 mm 5 mm −2.5 0.003 0.006 −2.25 0.004 0.007 −20.006 0.008 −1.75 0.007 0.010 −1.5 0.008 0.015 −1.25 0.013 0.026 −10.022 0.048 −0.75 0.046 0.090 −0.5 0.105 0.166 −0.25 0.237 0.276 0 0.4310.387 0.25 0.552 0.428 0.5 0.496 0.439 0.75 0.387 0.500 1 0.363 0.4941.25 0.355 0.361 1.5 0.282 0.218 1.75 0.188 0.120 2 0.112 0.060 2.250.059 0.029 2.5 0.028 0.015

TABLE 17 The through focus performance of Iteration G1, for both 5 mmand 4 mm pupil sizes, on candidate eye with an inherent primaryspherical aberration C(4,0) of 0.20 μm of the candidate eye measured at5 mm pupil. Defocus 4 mm 5 mm −2.5 0.005 0.008 −2.25 0.006 0.010 −20.008 0.013 −1.75 0.009 0.018 −1.5 0.012 0.029 −1.25 0.019 0.049 −10.035 0.080 −0.75 0.067 0.129 −0.5 0.123 0.205 −0.25 0.230 0.301 0 0.4090.385 0.25 0.561 0.415 0.5 0.546 0.393 0.75 0.412 0.410 1 0.339 0.4731.25 0.326 0.407 1.5 0.264 0.227 1.75 0.170 0.098 2 0.099 0.040 2.250.050 0.014 2.5 0.021 0.004

Section 16: Exemplary Sets of Designs as Intra-Ocular Lenses

Aberration profiles may be used in intra-ocular lens applications,according to certain embodiments. For example, the aberration profile,and/or power profile, may be translated into an intra-ocular lenssurface profile, using one or more of the following parameters:thickness profile, power profile, aberration profile, front surface,back surface, diameter, and/or refractive index of the material. Thesurface profile is thereafter provided to a computer assisted or othermanufacturing process to produce the intra-ocular lens. The intra-ocularlens produced is configured based at least in part on the surfaceprofile and/or surface profiles generated. In some embodiments, asupplementary intraocular lens may be implanted within an accommodatinggel during a post-lens extraction procedure (e.g. lens refillingsurgical procedure. The lens power profile (Iteration J1) shown in FIG.74 is a combination of Zernike higher order spherical aberration terms.The power profile may be converted to an axial thickness profile (FIG.75) for an intra-ocular lens, taking into account the refractive indexof the intra-ocular lens material, according to certain embodiments.Here, the refractive index of intra-ocular lens material is 1.475. Table18 provides the defocus term and other combinations of sphericalaberration terms, denoted in Zernike coefficients C(2,0) to C(20,0),that represent an exemplary design of an intra-ocular lens (FIG. 74) at4 and 5 mm optic zone diameter.

TABLE 18 Defocus and higher order spherical aberration coefficients, at4, and 5 mm optic zone diameter or pupil size, for one of the exemplaryembodiment of an intra-ocular lens design that provides an improvementin the through-focus optical and/or visual performance of the candidateeye. Iteration J1 Optic zone or Pupil size C(2,0) C(4,0) C(6,0) C(8,0)C(10,0) C(12,0) C(14,0) C(16,0) C(18,0) C(20,0) At 4 mm 12.060 −0.120−0.085 0.033 0.058 −0.018 −0.023 0.012 0.005 −0.003 At 5 mm 18.666−0.129 0.040 0.018 −0.089 −0.026 0.056 −0.006 −0.019 0.017

Section 16.A: Multi-Element IOLs

The aberration profiles disclosed herein may be used in multi-elementintra-ocular lens devices, for example, phakic and pseudophakicintra-ocular lens. The aberration profiles disclosed herein may be usedin multi-element intra-ocular lens devices to restore accommodation. Forexample, the aberration profile may be implemented on one or moreelements of the multi-element intra-ocular lens device, by manipulationof one or more of the following parameters of one or more of theelements: thickness profile, power profile, aberration profile, frontsurface, back surface, spacing between elements and refractive index.The parameters are thereafter provided to a computer assisted or othermanufacturing process to produce the multi-element intra-ocular lensdevice. These processes may include lathing, moulding, etching, ablatingand/or other methods. In certain embodiments, the profiles may becreated after the lens has been implanted. The intra-ocular lensproduced is configured based at least in part on the aberration profileand/or parameters generated.

Due to the multi-dimensional variable space in multi-elementintra-ocular lenses, for example, four surfaces in two element designs,the greater number of degrees of freedom provide greater designflexibility and greater number of design solutions. In addition, due tothe dynamic configuration of intra-ocular lenses, the distance betweenthe elements changes from distance to near focus, performance may bealtered and/or tailored by selection of appropriate aberration profileson different surfaces of the multi-element intra-ocular lens. One of thebenefits of the aberration profiles disclosed herein is that they may beused with multi-element intra-ocular lenses to provide differentperformances for distance, intermediate and near vision. For example,one may configure the elements for optimum visual performance atdistance and extended depth of focus at near range. The visualperformance may be visual acuity, contrast sensitivity, minimalghosting, or combinations thereof.

Section 17: Descriptors for Power Profiles with Use of a FourierTransform

Fourier transform methods may be used to characterise the power profilesof certain embodiments and in particular for certain bifocal ormultifocal designs. For example, FIG. 76 plots the power profiles for anumber of commercially available bifocal and multifocal lenses. FIG. 77plots the power profiles for a number of bifocal or multifocal lensesaccording to embodiments. FIG. 78 plots the Fourier transform of thepower profiles for the commercially available bifocal and multifocallenses of FIG. 76. FIG. 79 plots Fourier transforms of power profiles ofFIG. 77. For both FIGS. 78 and 79, the horizontal axis representsspatial frequency in cycles per millimetre (cycles/mm) and the verticalaxis plots the normalised absolute of the amplitude spectrum from thefast Fourier transform of the power profiles. In these figures,normalised means rescaling of each amplitude spectrum so that themaximum value for the absolute of an amplitude spectrum is rescaledto 1. For example, the normalised absolute of the amplitude spectrum maybe obtained by dividing the absolute of amplitude spectrum by themaximum value of the absolute of amplitude spectrum.

A comparison of FIGS. 78 and 79 illustrate differentiation betweencertain embodiments and the plotted commercially available lenses, astheir normalised absolute amplitude of the Fourier transform of theirpower profiles has normalised absolute amplitude greater than 0.2 at oneor more spatial frequencies at or above 1.25 cycles per millimetre. Incontrast to the illustrated embodiments FIGS. 77 and 79, none of thecurrently available commercial lenses have normalised absolute amplitudegreater than 0.2 at one or more spatial frequencies at or above 1.25cycles per millimetre. Certain embodiments such as lenses, bifocallenses, and/or multifocal lenses may be characterised using Fouriertransform. For example, certain embodiments are directed to a lenscomprising: an optical axis; at least two surfaces; wherein the lens ischaracterised by a power profile that has a normalised absoluteamplitude of the Fourier transform of the power profile that is greaterthan 0.2 at one or more spatial frequencies at or above 1.25 cycles permillimetre. In certain applications, the lens is configured with a powerprofile that has a normalised absolute amplitude of the Fouriertransform of the power profile that is greater than 0.2 at one or morespatial frequencies at or above 1.25 cycles per millimetre.

Section 18: Descriptors of Power Profiles Using First Derivatives orRate of Change of Power

First derivatives methods may be used to characterise the power profilesof certain embodiments, and in particular, for certain bifocal ormultifocal designs. For example, FIG. 76 plots the power profiles for anumber of commercially available bifocal and multifocal lenses. FIG. 77plots the power profiles for a number of multifocal lenses according toembodiments. FIG. 80 plots the first derivative of the power profilesfor the commercially available bifocal and multifocal lenses of FIG. 76.FIG. 81 plots the first derivative of power profiles of FIG. 77. Forboth FIGS. 80 and 81, the horizontal axis represents half-chord of theoptic zone diameter and the vertical axis plots the absolute of thefirst derivative of the power profiles.

A comparison of FIGS. 80 and 81 illustrates differentiation betweencertain embodiments and the plotted commercially available lenses, asthe absolute of the first derivative of the power profiles of theillustrated embodiments have at least 5 peaks whose absolute amplitudeis greater than 0.025 with units of 1D per 0.01 mm. In contrast to theillustrated embodiments FIGS. 80 and 81, none of the currently availablecommercial lenses have at least 5 peaks with absolute first derivativegreater than 0.025 with units of 1D per 0.01 mm.

Certain embodiments such as lenses, bifocal lenses, and/or multifocallenses may be characterised using first derivative or rate of change ofpower. For example, certain embodiments are directed to a lenscomprising: an optical axis; at least two surfaces; wherein the lens hasa power profile, the power profile is characterised such that theabsolute of a first derivative of the power profile has at least 5 peakswhose absolute amplitude is greater than 0.025 with units of 1D per 0.01mm along its half-chord. In certain applications, the at least one powerprofile is characterised such that the absolute of a first derivative ofthe power profile has at least 5 peaks whose absolute amplitude isgreater than 0.025 with units of 1D per 0.01 mm along its half-chord.

Section 19: Descriptors of Power Profiles with Use of AperiodicFunctions

Certain embodiments of the present disclosure have one or more powerprofiles that may be characterised by aperiodic functions over asubstantial portion of the half-chord optical zone of the lens. Certainembodiments are directed to lenses that are configured such that the atleast one power profile is aperiodic over a substantial portion of thehalf-chord optical zone of the lens. In general terms, an aperiodicfunction is defined as a function that is not periodic. A periodicfunction is a function that repeats or duplicates its values in regularintervals, often denoted as periods. For example, trigonometricfunctions (i.e. sine, cosine, secant, cosecant, tangent and cotangentfunctions) are periodic as their values are repeated over intervals of2π radians. A periodic function can also be defined as a function whosegraphical representation exhibits translational symmetry. A functionF(x) is said to be periodic with a period P (where P is a non-zeroconstant), if it satisfies the following condition: F(x+P)=F(x).

Section 20: Descriptors of Power Profiles with Use of Non-MonotonicFunctions

Certain embodiments of the present disclosure have one or more powerprofiles that may be characterised by non-monotonic functions over asubstantial portion of the half-chord optical zone of the lens. Certainembodiments are directed to lenses that are configured such that the atleast one power profile is non-monotonic over a substantial portion ofthe half-chord optical zone of the lens. In general terms, a ‘monotonic’or ‘monotone’ function is a function which either is substantiallynon-increasing or substantially non-decreasing. A function F(x) is saidto be non-increasing on an interval I of real numbers if: F(b)<=F(a) forall b>a; where a, b are real numbers and are a subset of I; A functionF(x) is said to be non-decreasing on an interval I of real numbers if:F(b)>=F(a) for all b>a; where a, b are real numbers and are a subset ofI.

Section 21: Descriptors of Power Profiles with Use of Non-Monotonic andAperiodic Functions

Certain embodiments of the present disclosure have one or more powerprofiles that may be characterised by non-monotonic and aperiodicfunctions over a substantial portion of the half-chord optical zone ofthe lens. Certain embodiments are directed to lenses that are configuredsuch that the at least one power profile is non-monotonic and aperiodicover a substantial portion of the half-chord optical zone of the lens.In general, some functions may be both non-monotonic and aperiodic. Suchfunctions possess properties of both non-monotonic and aperiodicfunction as described herein.

Certain embodiments such as lenses, bifocal lenses, and/or multifocallenses may be characterised using aperiodic function, non-monotonicfunction, or combinations thereof. A lens comprising: an optical axis;at least two surfaces; wherein the lens has at least one power profile,the power profile is characterised by a function that is non-monotonic,aperiodic or combinations thereof over a substantial portion of thehalf-chord optical zone of the lens. In certain applications, the lensis configured with a power profile that is non-monotonic, aperiodic orcombinations thereof over a substantial portion of the half-chordoptical zone of the lens.

Section 22: Power Profile of Lenses

As is apparent from a visual inspection of at least FIGS. 19, 20, 22-25,29, 31, 34, 35, 39, 40, 41, 56-60 and 68, certain embodiments have apower profile that has the following combination of characteristicsacross half-chord diameters:

(i) A power profile that has a moving average that either increases withdiameter and then decreases, or decreases with diameter or thenincreases. For certain contact lens embodiments, the moving average maybe calculated over a window of 1 mm from on-axis to about 4 mm.Accordingly, by way of example, the average value may be calculatedacross the range of on-axis to 1 mm, and recalculated at intervalsselected from the group of 0.2 mm, 0.4 mm or 0.6 mm.(ii) A power profile with transitions between local minima and maximawithin a 1 mm change of radius at least 4 times across a 4 mm of thehalf-chord. For example, referring to FIG. 22, the power profile startsat a local maximum on-axis and transitions to a local minimum at about 1mm radius; the transitions between local maxima and minima then occur atabout 1.6 mm and about 2.3 mm. After that, the power profile may eitherhave the next local minima at about 2.9 mm, a local minimum at about 3.1mm and a local maximum at about 4 mm, or have the next local maximum atabout 4 mm. In some examples, the power profile transitions at least 6times across a 4 mm of the half-chord. For example, referring to FIG.24, there are two transitions in the first 1 mm radius, two in thesecond 1 mm radius, and two transitions in the region from 2 mm to 4 mm.In some examples the power profile transitions at least 8 times acrossthe 4 mm radius range (for example FIG. 29) or at least 12 times acrossthe 4 mm radius range (for example FIG. 35) or at least 15 times (forexample FIG. 40).(iii) The power profile transitions smoothly out to a radius selectedfrom the group of at least 3 mm, at least 3.5 mm and at least 4 mm.

Accordingly, certain embodiments have a power profile with a combinationselected from the options within (i) and (ii) and (iii), which providesacceptable vision for at least a subset of a population. Theseembodiments may have application to myopia, hyperopia, and/orpresbyopia, with or without astigmatism. Other embodiments include acombination from the options described above in this section 22,together with one or more of:

(iv) The refractive power on-axis power differs from the prescriptionpower by at least about 0.7D (e.g. see FIG. 22), or by at least about1.5 D (e.g. see FIG. 38).(v) The difference between the global maximum and global minimum poweris between approximately 1.5 to 2.5 times the difference between anyadjacent local minimum and local maximum within a radius of about 2.5mm. In other words, the global maximum and global minimum are reachedthrough a stepped change in power profile, that itself transitionsbetween local minima and local maxima.

Section 23: Clinical Performance of Some Exemplary Embodiments Comparedwith Commercially Available Single Vision, Bifocal and Multifocal SoftContact Lenses

In the following experimental clinical study, performance of fourexemplary embodiments described herein (manufactured into the form ofsoft contact lenses) were compared against seven commercially availablelenses including one single vision, one bifocal and five multifocalproducts whose details are provided in the table herein, Table 19. Thestudy was approved by ethics committee of Bellberry, South Australia.

Experimental Purpose:

The aim of the study was to assess the visual performance of fourmultifocal soft contact lenses, according to certain embodiments, andsix commercially available bifocal and multifocal lens designs.

Study Design:

The study design was a prospective, participant-masked, bilateral wear,cross-over clinical trial with a minimum overnight washout periodbetween the lens assessments. Lens wear duration was up to 2 hours.

Participant Selection:

Participants were included in the study if they met the followingcriterion:

a) Able to read and comprehend English and give informed consent asdemonstrated by signing a record of informed consent.b) Be at least 18 years old, male or female (the results reported hereinare for participants over 45 years).c) Willing to comply with the wearing and clinical trial visit scheduleas directed by the Investigator.d) Have ocular health findings within normal limits which would notprevent the participant from safely wearing contact lenses.e) Is correctable to at least 6/6 (20/20) or better in each eye withsingle vision contact lenses.f) Have an astigmatism correction of −1.5 D or less.g) Be experienced or inexperienced at wearing contact lenses.

Participants were excluded from the study if they had one or more of thefollowing conditions:

a) Pre-existing ocular irritation, injury or condition (includinginfection or disease) of the cornea, conjunctiva or eyelids that wouldpreclude contact lens fitting and safe wearing of contact lenses.b) Systemic disease that adversely affected ocular health e.g. diabetes,Graves disease, and auto immune diseases such as ankylosing spondylitis,multiple sclerosis, Sjögrens syndrome and systemic lupus erythematosus.Note: Conditions such as systemic hypertension and arthritis would notautomatically exclude prospective participants.c) Use of or a need for concurrent category S3 and above ocularmedications at enrolment and/or during the clinical trial.d) Use of or a need for systemic medication and/or topical medicationswhich may alter normal ocular findings and/or are known to affect aparticipant's ocular health and/or physiology or contact lensperformance either in an adverse or beneficial manner at enrolmentand/or during the clinical trial.e) NB: Systemic antihistamines are allowed on an “as needed basis”,provided they are not used prophylactically during the trial and atleast 24 hours before the clinical trial product is used.f) Eye surgery within 12 weeks immediately prior to enrolment for thistrial.g) Previous corneal refractive surgery.h) Contraindications to contact lens wear.i) Known allergy or intolerance to the ingredients of the clinical trialproducts.j) The investigators excluded anyone who they believe may not be able tofulfil the clinical trial requirements.

TABLE 19 List of the lenses used in the clinical study Mode Contact ofLenses Wear Base Lens (Marketed in in this Power Diameter Curve CodeAustralia as) Manufacturer Material Trial (D) (mm) (mm) Lens AirOptix ®Alcon (USA) Lotrafilcon Daily +4.00D to 14.2 8.6 A Aqua Single B wear−10.00 vision Lens Air Optix ® CIBA VISION Lotrafilcon Daily +6.00D to14.2 8.6 B Aqua (USA) B Wear −1.00D Multifocal Low/Med/High LensACUVUE ® J&J (USA) Etafilcon A Daily +6.00D to 14.2 8.5 C Bifocal Wear−9.00D +1.50/+2.50D Lens Proclear ® Cooper Vision Omafilcon Daily +4.00Dto 14.4 8.5 to D Multifocal- (USA) A wear −10.00D 8.7 Distance Low/Highdesign Lens Proclear ® Cooper Vision Omafilcon Daily +4.00D to 14.4 8.5to E Multifocal- (USA) A wear −10.00D 8.7 Near design Low/High LensPureVision ® Bausch & Balafilcon Daily +6.00D to 14.0 8.6 F multifocalLomb (USA) A wear −10.00D Low/High Lens CLARITI ® 1 Sauflon (UK) FilconII Daily +5.00D to- 14.1 8.6 G Day multifocal multifocal wear −6.00Low/High Lens Prototype 1 Lathe Hioxifilcon Daily +4.00D to 13.5 8.1 toH Manufactured A/B/D wear −10.00D to 8.7 14.5 Lens Prototype 2 LatheHioxifilcon Daily +4.00D to 13.5 8.1 to I Manufactured A/B/D wear−10.00D to 14.5 8.7 Lens Prototype 3 Lathe Hioxifilcon Daily +4.00D to13.5 8.1 to J Manufactured A/B/D wear −10.00D to 14.5 8.7 Lens Prototype4 Lathe Hioxifilcon Daily +4.00D to 13.5 8.1 to K Manufactured A/B/Dwear −10.00D to 14.5 8.7

Methods:

For each fitting visit, lenses were fitted bilaterally. After allowingfor the lenses to settle, lens performance was assessed including:

1. Visual acuity

a. Log MAR charts were used to obtain measurements for vision atdistance under high illumination conditionsb. High contrast visual acuity at 6 metresc. Low contrast visual acuity at 6 metresd. Contrast sensitivity using a Pelli-Robson equivalent chart (usingThomson software) equivalent at 6 metres, the text was kept constant at6/12 letter size while the contrast was reduced as a logarithmicfunction.e. Hanks near point chart was used to measure visual acuity at 70 cm(intermediate vision), at 50 cm and 40 cm (near vision) under highillumination conditions. As the Hanks near point chart was designed tobe used at 40 cm near, the visual acuity equivalents for 50 cm and 70 cmwere calculated. Both intermediate and near visual acuity results wereconverted to equivalent log MAR

Subjective Response Questionnaire:

1. Quality of distance, intermediate and near vision on a visualanalogue scale of 1 to 10.2. Rating of distance and near ghosting on a ghosting analogue scale of1 to 10.3. Overall rating of vision performance on a visual analogue scale of 1to 10.

FIGS. 82 to 108 show the subjective and objective results obtained fromthe clinical study. The distance, intermediate, near and over all visionratings were measured on a visual analogue scale ranging from 1 to 10 insteps of 1, where 1 represented blurred and/or hazy vision and 10represented clear and/or sharp vision. The ghosting vision rating atdistance and near were measured on a ghosting visual analogue scaleranging from 1 to 10 in steps of 1, where 1 represented no ghostingand/or doubling and 10 represented extreme ghosting and/or doubling. Thelack of ghosting was calculated by subtracting ghosting score from 11points. Cumulative vision results were obtained by averaging thedistance, intermediate and near vision results. Cumulative ghostingresults were obtained by averaging the ghosting at distance and neardistances.

Section 24: Descriptors of Power Profiles with Use of Zernike PowerPolynomials

When a monochromatic wavefront W (ρ, θ) of an optical system isprovided, where ρ is the radial distance and θ is the angle in polarco-ordinates, an estimate of the refractive power distribution of thewavefront can be defined as:

${P( {\rho,\theta} )} = \frac{1000}{{W( {\rho,\theta} )} + {r( \frac{\partial{W( {\rho,\theta} )}}{\partial r} )}^{- 1}}$

Where ‘∂W/∂r’ represents partial derivative of W (ρ, θ) along the radialdistance ‘r’. If the monochromatic wavefront W (ρ, θ) is chosen to bedescribed as a finite series of standard Zernike polynomial expansion,the wavefront-based refractive power may be represented by a set ofbasic functions and the original set of the wavefront standard Zernikepolynomial coefficients, as shown below:

${P( {\rho,\theta} )} = {\frac{1000}{r_{\max}}{\sum\limits_{j = 3}^{p - 1}{c_{j}{\psi_{j}( {\frac{r}{r_{\max}},\theta} )}}}}$

Where r_(max) corresponds to the pupil radius;

${\psi_{j}( {\rho,\theta} )}\{ \begin{matrix}{{( \sqrt{2( {n + 1} )} )\mspace{14mu} {R_{n}^{m}(\rho)}{\cos ( {m\; \theta} )}};} & {{{if}\mspace{14mu} m} > 0} \\{{( \sqrt{2( {n + 1} )} )\mspace{11mu} {R_{n}^{m}(\rho)}\; {\sin ( {m\; \theta} )}};} & {{{if}\mspace{14mu} m} < 0} \\{{( \sqrt{( {n + 1} )} )\mspace{14mu} {R_{n}^{m}(\rho)}};} & {{{if}\mspace{14mu} m} = 0}\end{matrix} $

Where

${R_{n}^{m}(\rho)} = {\sum\limits_{s = 0}^{{(\frac{n - {m}}{2})} - q}{\frac{{- 1^{s}}( {( {n - s} )!} )( {n - {2s}} )}{{s!}( {( {\frac{n + {m}}{2} - s} )!} )( {( {\frac{n - {m}}{2} - s} )!} )}( \rho^{n - {2s} - 2} )}}$

Where

$q = \{ \begin{matrix}{1,} & {{{if}\mspace{14mu} {m}} \leq 1} \\{0,} & {otherwise}\end{matrix} $

Where n and m are radial and azimuthal components in a double indexnotation of Zernike polynomial and j is the Zernike coefficient in asingle index notation scheme.

For example, list of rotationally symmetric Zernike power polynomialexpansions up to 10^(th) order i.e. 5 rotationally symmetric terms arelisted below:

P=Z1*4*3̂(½)+

Z2*5̂(½)*(24*R̂2−12)+

Z3*7̂(½)*(120*R̂4−120*R̂2+24)+

Z4*9̂(½)*(360*R̂2−840*R̂4+560*R̂6−40)+

Z5*11″(½)*(3360*R̂4−840*R̂2−5040*R̂6+2520*R̂8+60)

Power distribution=(1/r _(max)̂2)*P

The terms Z1, Z2, Z3, Z4 and Z5 in the above Zernike power polynomialexpansion represent C(2,0), C(4,0), C(6,0), C(8,0) and C(10,0)coefficients, respectively.

Zernike power polynomials as described herein may be used tocharacterise the power profiles of certain embodiments. FIGS. 124 to 127show the designed power profiles for some exemplary embodiments. FIGS.119 to 123 show the power profiles for some commercially availablemultifocal lenses as measured on a commercially available Hartman-Shackbased power profiling instrument named Optocraft (Optocraft Gmbh,Germany). Default settings for use of a multifocal lens were used toobtain measured data for commercial lenses. The commercial lenses weresymmetric and only a cross section of the power profile was exported forthe Zernike power polynomial fit analysis. In this example, the datadensity, i.e., the number of points used for the fitting analysis waswere 400 from 0 to 4 mm in 0.01 mm steps on a half-chord of the opticzone of the lens. The same data density was used when fitting theexemplary embodiments to Zernike power polynomials. A least squareapproach was used to optimise the best coefficients for the chosendegree/order of the symmetric radial Zernike power polynomial. Once theoptimisation routine was completed, the computational routine hasresulted in two metrics, coefficient of determination (R²) and root meansquare error (RMSE), the smaller the RMSE, the better the fit and thehigher the R² value, the better the fit. As used in this example, bestfit means a fit with the lowest order mathematical function that resultsin a coefficient of determination (R²) greater than 0.975 and/or a rootmean square error (RMSE) less than 0.15D. In cases where theoptimisation procedure fails to fit a function that achieves thecriteria of R²>0.975 and RMSE<0.15D, then the order of the function thatproduces the greatest R² and/or the lowest RMSE is used to characterisethe power profile. However, such power profiles in this example do notmeet the criteria of the exemplary embodiments. Certain embodiments maybe characterised using radial Zernike power polynomials. Differencesbetween conventional multifocals and exemplary embodiments are shown intables 20 to 23. As shown in the tables 20 to 23, the number ofsubstantially non-zero, symmetric, Zernike power polynomial coefficientsrequired to best fit the power profiles of the exemplary embodiments isgreater than the number of substantially non-zero, symmetric, Zernikepower polynomial coefficients required to fit the power profiles of themeasured conventional multifocals. As used in this example, best fitmeans a fit with the lowest order mathematical function that results ina coefficient of determination (R²) greater than 0.975 and/or a rootmean square error (RMSE) less than 0.15D. In cases where theoptimisation procedure fails to fit a function that achieves thecriteria of R²>0.975 and RMSE<0.15D, then the order of the function thatproduces the greatest R² and/or the lowest RMSE is used to characterisethe power profile. However, such power profiles in this example do notmeet the criteria of the exemplary embodiments. As shown in tables 20and 21, the conventional lenses are described by less than 20coefficients which are non-zero (from C(2,0) to C(40,0)) as comparedwith the exemplary designs which are described by at least 20 non-zerocoefficients. As can be seen from the values of R² and RMSE in table 21,the commercial designs multifocal 7 and multifocal 8 were reproducedwith RMSE>0.25D using Zernike power polynomials. In contrast, the R² andRMSE values of the exemplary embodiments 1 to 8 were reproduced withRMSE<0.15D using Zernike power polynomials (tables 22 and 23) provided asufficient number of coefficients were used in the calculations.

TABLE 20 Zernike Power Polynomial Coefficients-Commercial multifocalsMultifocal Multifocal Multifocal Multifocal Multifocal MultifocalCoefficients 1 2 3 4 5 6 C(2,0) −2.000E+00 −1.730E+00   7.670E−01−5.302E−01   6.207E−01 −5.644E−01 C(4,0) −8.010E−01 −7.475E−01−5.321E−01 −4.660E−01 −5.859E−01 −5.275E−01 C(6,0)   4.681E−02  5.715E−02   2.280E−01   1.400E−01   1.509E−01   1.542E−01 C(8,0)−4.288E−02   3.339E−02 −1.358E−01 −1.019E−01 −6.840E−02   6.215E−03C(10,0)   2.526E−02   1.053E−02   5.091E−02   5.116E−02 −2.945E−02−4.029E−02 C(12,0) −1.937E−02 −1.596E−03 −4.997E−03 −3.214E−03−1.958E−02 −1.114E−02 C(14,0)   3.941E−03 −3.284E−03 −5.050E−03−1.427E−02   1.867E−02   7.429E−03 C(16,0) −7.450E−04 −5.524E−05  1.852E−02   1.834E−02   2.936E−03   3.334E−03 C(18,0) −1.941E−03  1.374E−04 −7.779E−03 −1.267E−03 −9.033E−03   7.043E−04 C(20,0)  3.780E−03 −3.422E−04 −3.408E−03 −5.439E−03   8.539E−04 −2.187E−03C(22,0) 0 0 0 0 0 0 C(24,0) 0 0 0 0 0 0 C(26,0) 0 0 0 0 0 0 C(28,0) 0 00 0 0 0 C(30,0) 0 0 0 0 0 0 C(32,0) 0 0 0 0 0 0 C(34,0) 0 0 0 0 0 0C(36,0) 0 0 0 0 0 0 C(38,0) 0 0 0 0 0 0 C(40,0) 0 0 0 0 0 0 C(42,0) 0 00 0 0 0 C(44,0) 0 0 0 0 0 0 C(46,0) 0 0 0 0 0 0 C(48,0) 0 0 0 0 0 0C(50,0) 0 0 0 0 0 0 C(52,0) 0 0 0 0 0 0 C(54,0) 0 0 0 0 0 0 C(56,0) 0 00 0 0 0 C(58,0) 0 0 0 0 0 0 C(60,0) 0 0 0 0 0 0 C(62,0) 0 0 0 0 0 0C(64,0) 0 0 0 0 0 0 C(66,0) 0 0 0 0 0 0 C(68,0) 0 0 0 0 0 0 C(70,0) 0 00 0 0 0 R-Square 1.00 1.00 1.00 1.00 1.00 1.00 RMSE 0.04 0.00 0.04 0.020.03 0.01Table 20 shows the values of the rotationally symmetric coefficientswhen radial Zernike power polynomials are fitted to the power profilesdescribed in FIGS. 119 and 120 via non-linear least square optimisationroutine.

TABLE 21 Zernike Power Polynomial Coefficients - Commercial multifocalsCoefficients Multifocal 7 Multifocal 8 Multifocal 9 Multifocal 10 C(2,0)2.000E+00 2.000E+00 −3.513E−01 −1.031E+00 C(4,0) 2.373E−01 −9.382E−03−2.129E−01 −1.436E−01 C(6,0) −2.674E−01 −1.370E−01 2.835E−01 1.933E−01C(8,0) 1.339E−01 8.387E−02 −8.365E−02 −6.085E−02 C(10,0) −1.370E−02−1.971E−02 −9.280E−03 1.546E−03 C(12,0) −4.285E−02 −1.437E−02 1.689E−026.472E−03 C(14,0) 4.462E−02 2.032E−02 −4.245E−03 −3.095E−03 C(16,0)−1.898E−02 −1.025E−02 −6.685E−03 −1.626E−03 C(18,0) −2.518E−03 2.929E−055.956E−03 −9.733E−05 C(20,0) 9.978E−03 5.319E−03 1.080E−03 1.764E−03C(22,0) −5.685E−03 −3.982E−03 −5.456E−03 −2.246E−03 C(24,0) −1.051E−037.688E−04 2.668E−03 −5.335E−04 C(26,0) 4.671E−03 1.396E−03 7.324E−042.846E−03 C(28,0) −2.796E−03 −1.348E−03 −2.197E−03 −1.714E−03 C(30,0)−4.901E−04 3.974E−04 1.157E−03 −8.392E−04 C(32,0) 2.376E−03 3.274E−044.228E−03 2.467E−03 C(34,0) −1.938E−03 −3.972E−04 −5.684E−03 −6.234E−04C(36,0) 5.063E−04 −6.133E−05 −8.093E−03 −6.723E−03 C(38,0) 3.930E−042.413E−04 5.137E−03 1.647E−03 C(40,0) −5.948E−04 −2.563E−04 3.633E−033.610E−03 C(42,0) 0 0 0 0 C(44,0) 0 0 0 0 C(46,0) 0 0 0 0 C(48,0) 0 0 00 C(50,0) 0 0 0 0 C(52,0) 0 0 0 0 C(54,0) 0 0 0 0 C(56,0) 0 0 0 0C(58,0) 0 0 0 0 C(60,0) 0 0 0 0 C(62,0) 0 0 0 0 C(64,0) 0 0 0 0 C(66,0)0 0 0 0 C(68,0) 0 0 0 0 C(70,0) 0 0 0 0 R-Square 0.92 0.99 0.99 0.99RMSE 1.02 0.32 0.07 0.05Table 21 shows the rotationally symmetric coefficients when radialZernike power polynomials are fitted to the power profiles described inFIGS. 119 and 120 via non-linear least square optimisation routines.

TABLE 22 Zernike Power Polynomial Coefficients-Exemplary embodimentsCoefficients # 1 # 2 # 3 # 4 # 5 # 6 C(2,0)   2.701E−01   1.090E−01  4.976E−01 −2.451E−01 −7.169E−02   7.998E−01 C(4,0)   9.265E−03−1.897E−01 −4.803E−01 −2.952E−01 −3.958E−01 −4.814E−01 C(6,0)  1.650E−01   1.287E−01 −2.196E−02   6.502E−02   6.074E−02 −3.564E−02C(8,0)   4.288E−02 −2.355E−02   4.919E−02   4.613E−02   7.780E−02  7.893E−02 C(10,0)   3.964E−02 −4.354E−02   1.352E−02 −5.739E−02−6.837E−02 −6.449E−03 C(12,0)   8.367E−02   5.164E−02   1.895E−02−6.077E−02 −8.238E−02 −1.187E−01 C(14,0)   4.264E−02   2.743E−03  6.990E−02   6.374E−02   8.132E−02   4.934E−02 C(16,0) −5.268E−03−4.641E−02   4.742E−02 −4.232E−03   9.194E−04   3.829E−02 C(18,0)  5.682E−02   4.436E−02   4.552E−02 −4.960E−02 −6.504E−02 −6.596E−02C(20,0)   1.639E−02 −7.830E−03 −2.472E−02   2.458E−02   2.871E−02  5.812E−04 C(22,0) −8.215E−03 −2.349E−02   1.697E−02   1.986E−02  3.005E−02   4.089E−02 C(24,0)   2.697E−02   3.900E−02   3.630E−02−3.311E−02 −4.169E−02 −2.929E−02 C(26,0)   1.995E−03   3.267E−03−4.724E−02   3.313E−03   2.996E−03 −2.071E−02 C(28,0) −5.664E−03  2.797E−03   3.182E−03   2.268E−02   3.177E−02   3.920E−02 C(30,0)  1.375E−02   3.423E−02   3.652E−02 −2.046E−02 −2.729E−02 −2.058E−02C(32,0) −1.324E−03 −1.079E−03 −2.749E−02   2.766E−03   2.571E−03−1.174E−02 C(34,0)   3.083E−03   2.599E−03   9.379E−03   1.049E−02  1.431E−02   2.986E−02 C(36,0)   7.837E−03   1.043E−02   3.214E−02−1.021E−02 −1.326E−02 −2.012E−02 C(38,0) −4.608E−03 −1.179E−02−1.855E−02   2.176E−03   2.590E−03   1.829E−03 C(40,0)   1.366E−03  2.618E−03   6.700E−03   2.759E−03   2.657E−03   4.219E−03 C(42,0)−2.510E−03 −1.903E−03   3.675E−03   3.145E−03   7.994E−03 −9.116E−04C(44,0) −2.890E−03 −5.774E−03 −8.602E−03 −2.827E−03 −4.593E−03  3.930E−03 C(46,0) −4.175E−03   2.191E−03   5.087E−03 −1.646E−03−5.412E−03 −1.896E−03 C(48,0) −9.448E−03 −4.915E−03 −1.174E−02  1.578E−03   2.248E−03   5.931E−04 C(50,0) −1.229E−03   1.698E−04−7.154E−03 −2.359E−04 −9.947E−05 −7.696E−04 C(52,0)   6.378E−05  2.473E−05 −3.380E−04 −1.371E−05 0 0 C(54,0) −2.373E−05 −1.326E−04−9.104E−05   1.285E−06 0 0 C(56,0) −5.117E−06   9.333E−06 −7.328E−06  2.907E−07 0 0 C(58,0) −5.115E−07   3.441E−06 −2.362E−06   9.186E−08 00 C(60,0) −3.461E−07   5.216E−07 −6.425E−07 −3.161E−09 0 0 C(62,0)−6.527E−09   7.916E−08 −1.240E−08 0 0 0 C(64,0)   1.110E−08   2.701E−09  1.824E−08 0 0 0 C(66,0)   2.215E−09 −1.140E−09   4.189E−09 0 0 0C(68,0) −3.861E−11   7.350E−10 −1.738E−10 0 0 0 C(70,0) −9.018E−11  2.412E−10 −1.065E−10 0 0 0 R-Square 0.989 0.987 0.978 0.996 0.9930.997 RMSE 0.053 0.091 0.120 0.037 0.071 0.052Table 22 snows the rotationally symmetric coefficients when radialZernike power polynomials are fitted to the power profiles described inFIGS. 119 and 120 via non-linear least square optimisation routines.

TABLE 23 Zernike Power Polynomial Coefficients-Exemplary embodimentsCoefficients # 7 # 8 # 9 # 10 # 11 # 12 C(2,0) −2.718E−01   3.513E−02  9.938E−01   2.762E−01   4.384E−01   6.345E−01 C(4,0) −3.044E−01−2.457E−01 −4.241E−01 −1.478E−01 −3.311E−01 −6.140E−01 C(6,0)  2.888E−02   1.778E−01 −9.882E−03   1.035E−01   9.858E−03   4.338E−02C(8,0)   9.957E−03   1.454E−01   4.060E−02 −9.408E−02 −1.312E−01−8.419E−02 C(10,0) −4.792E−02   6.128E−03 −5.843E−02   4.744E−03−1.743E−02 −3.853E−03 C(12,0) −5.411E−02 −1.741E−02 −7.895E−02  5.040E−02   4.700E−02   6.687E−02 C(14,0)   3.068E−02   7.079E−02  4.684E−02 −1.064E−02 −6.289E−03   1.747E−02 C(16,0)   4.469E−03  2.097E−02   1.081E−02 −1.968E−02 −2.008E−02   2.461E−02 C(18,0)−3.885E−02 −4.246E−02 −6.860E−02 −1.601E−02 −1.649E−02 −2.264E−02C(20,0)   6.136E−03   1.631E−02   2.199E−02   3.810E−02   5.419E−02  5.810E−02 C(22,0)   2.392E−02   4.266E−02   3.962E−02   5.185E−04−6.705E−03   9.668E−03 C(24,0) −3.189E−02 −3.112E−02 −5.811E−02−4.185E−02 −7.439E−02 −9.184E−02 C(26,0) −2.211E−03   1.025E−02  9.437E−03   2.936E−02   2.953E−02   3.758E−02 C(28,0)   1.934E−02  4.138E−02   3.565E−02   6.849E−03 −1.677E−03   1.532E−02 C(30,0)−1.835E−02 −2.151E−02 −3.963E−02 −2.004E−02 −4.252E−02 −4.233E−02C(32,0)   9.752E−03   1.168E−02   1.381E−02   9.819E−03   5.167E−03  1.880E−02 C(34,0)   5.949E−03   1.950E−02   7.644E−03 −5.173E−04−3.188E−03   1.139E−02 C(36,0) −1.655E−02 −1.732E−02 −1.850E−02  6.727E−04   1.212E−03 −1.202E−03 C(38,0)   8.307E−03   2.627E−03  1.695E−02 −1.782E−03   2.440E−03 −1.835E−03 C(40,0)   2.834E−03−3.172E−03 −1.300E−02 −1.257E−03   1.807E−03   2.872E−03 C(42,0)−3.808E−04   1.470E−04   4.063E−03   6.737E−03   5.411E−03   3.155E−03C(44,0)   1.134E−04   5.987E−04   1.427E−02 −2.124E−03 −9.658E−04−5.987E−03 C(46,0)   9.160E−04 −7.718E−03 −2.066E−03 −4.028E−03  4.675E−03   1.837E−03 C(48,0)   9.550E−04 −3.049E−03 −3.622E−03  1.434E−03   4.284E−03   3.482E−03 C(50,0) −9.903E−04   1.617E−03−1.907E−03   3.087E−04 −2.538E−03 −3.251E−03 C(52,0) 0   2.347E−04 0 0−3.804E−04 −7.959E−04 C(54,0) 0 −5.306E−05 0 0   5.870E−05 −6.750E−05C(56,0) 0   2.745E−06 0 0 −8.670E−06 −3.545E−06 C(58,0) 0   2.304E−06 00 −3.880E−06 −1.224E−06 C(60,0) 0   1.550E−07 0 0 −4.224E−07 −1.016E−07C(62,0) 0   5.520E−08 0 0 −7.297E−08   4.568E−08 C(64,0) 0   5.160E−09 00 −2.535E−09   8.645E−09 C(66,0) 0 −7.325E−10 0 0   1.309E−09  1.429E−09 C(68,0) 0   2.637E−10 0 0 −5.515E−10 −4.969E−10 C(70,0) 0  6.793E−11 0 0 −1.313E−10 −2.628E−11 R-Square 0.991 0.990 0.976 0.9950.994 0.985 RMSE 0.064 0.088 0.158 0.033 0.045 0.094Table 23 shows the rotationally symmetric coefficients when radialZernike power polynomials are fitted to the power profiles described inFIGS. 119 and 120 via non-linear least square optimisation routines.

In certain embodiments, a lens comprising: an optical axis; at least twosurfaces; wherein the lens has a power profile, the power profile may bereproduced by using at least 30 or 40 non-zero, symmetric, Zernike powerpolynomial coefficients. In certain embodiments, the power profile maybe reproduced by using at least 28, 30, 40, 50, 60, 70 or 80 non-zero,symmetric, Zernike power polynomials. In certain embodiments, the powerprofile may be reproduced by using between 30 to 40, 30 to 50 or 40 to80 non-zero, symmetric, Zernike power polynomial coefficients. Incertain embodiments, the power profile may be reproduced by usingbetween 30 to 80, 30 to 70 or 30 to 50 non-zero, symmetric, Zernikepower polynomial coefficients. In some embodiments, one or more of theZernike power polynomial coefficients may be zero as long as the highestorder Zernike power polynomial coefficients is non-zero or substantiallynon-zero. For example, a 20^(th) order Zernike power polynomial may havea 20^(th) order Zernike power polynomial coefficient that is non-zero,or substantially non-zero, while at the same time one or more of theZernike power polynomial coefficients for orders below the 20^(th) mayhave zero value.

Section 25: Descriptors of Power Profiles with Use of Fourier Series

Fourier series expansion of the generic form is (rotationally symmetric)given below:

${P(\rho)} = {C + {\sum\limits_{i = 1}^{n}{a_{i}( {\cos (\rho)} )}} + {b_{i}( {\sin (\rho)} )}}$

where i=1 to n, where i is an integer and n is the order of Fourierseries considered; C is the constant; ρ is the radial co-ordinate ofpower profile; a_(i) and b_(i) are the coefficients of the Fourierexpansion of the i^(th) order.

Fourier series as described herein may be used to characterise the powerprofiles of certain embodiments. FIGS. 124 to 127 show the designedpower profiles for some exemplary embodiments. FIGS. 119 to 123 show thepower profiles for some commercially available multifocal lenses asmeasured on a commercially available Hartman-Shack based power profilinginstrument named Optocraft (Optocraft Gmbh, Germany). Default settingsfor use of a multifocal lens were used to obtain measured data forcommercial lenses. The commercial lenses were symmetric and a crosssection of the power profile was exported for the Fourier series fitanalysis. In this example, the data density, i.e. the number of pointsused for the fitting analysis was 400, from 0 to 4 mm in 0.01 mm stepson a half-chord of the optic zone of the lens. The same data density wasused when fitting the exemplary embodiments to Fourier series. A leastsquare approach was used to optimise the best coefficients for thechosen degree or order of the Fourier series. Once the optimisationroutine was completed, the computational routine has resulted in twometrics, coefficient of determination (R²) and root mean square error(RMSE), the smaller the RMSE, the better the fit and the higher the R²value, the better the fit. As used in this example, best fit means a fitwith the lowest order mathematical function that results in acoefficient of determination (R²) greater than 0.975 and/or a root meansquare error (RMSE) less than 0.15D. In cases where the optimisationprocedure fails to fit a function that achieves the criteria of R²>0.975and RMSE<0.15D, then the order of the function that produces thegreatest R² and/or the lowest RMSE is used to characterise the powerprofile. However, such power profiles in this example do not meet thecriteria of the exemplary embodiments. Tables 24 to 27 shows thecoefficient values of the Fourier series expansion up to 15^(th) orderobtained when the power profiles described in FIGS. 119 and 120 are bestfitted to the described Fourier series expansion via non-linear leastsquare optimisation routines. In this example, the conventional lensesare described by less than 4 orders of the Fourier series which havenon-zero coefficients, in contrast, the exemplary designs need at least8 orders of the Fourier series which have non-zero coefficients to bereproduced with an RMSE<0.15D.

In certain embodiments, a lens comprising: an optical axis; at least twosurfaces; wherein the lens has a power profile, the power profile may bereproduced by using at least 6, 8, 10, 12, 15^(th) order of the Fourierseries expansion which have substantially non-zero coefficients.

TABLE 24 Fourier Series Coefficients-Commercial multifocals MultifocalMultifocal Multifocal Multifocal Multifocal Multifocal Coefficients 1 23 4 5 6 C −0.408 −0.355 0.946 0.221 0.237 −0.067 a1 1.280 0.840 1.2871.011 0.793 0.657 b1 0.940 0.592 0.828 0.704 1.568 0.846 a2 0.493 0.0670.470 0.393 0.833 0.333 b2 −0.082 −0.179 0.358 0.219 0.410 0.114 a3 0 00 0 0.248 0.173 b3 0 0 0 0 −0.217 −0.164 a4 0 0 0 0 0 0 b4 0 0 0 0 0 0a5 0 0 0 0 0 0 b5 0 0 0 0 0 0 a6 0 0 0 0 0 0 b6 0 0 0 0 0 0 a7 0 0 0 0 00 b7 0 0 0 0 0 0 a8 0 0 0 0 0 0 b8 0 0 0 0 0 0 a9 0 0 0 0 0 0 b9 0 0 0 00 0 a10 0 0 0 0 0 0 b10 0 0 0 0 0 0 a11 0 0 0 0 0 0 b11 0 0 0 0 0 0 a120 0 0 0 0 0 b12 0 0 0 0 0 0 a13 0 0 0 0 0 0 b13 0 0 0 0 0 0 a14 0 0 0 00 0 b14 0 0 0 0 0 0 a15 0 0 0 0 0 0 b15 0 0 0 0 0 0 RSq 0.999 0.9990.996 0.993 0.995 0.998 RMSE 0.042 0.019 0.078 0.075 0.069 0.033Table 24 shows the values of the coefficients of the Fourier seriesexpansion (up to 15^(th) order) obtained when the power profilesdescribed in FIGS. 119 to 123 are best fitted to Fourier seriesexpansion via non-linear least square optimisation routines.

TABLE 25 Fourier Series Coefficients - Commercial multifocalsCoefficients Multifocal 7 Multifocal 8 Multifocal 9 Multifocal 10 C2.093 1.307 1.158 0.268 a1 −0.307 −0.071 1.551 1.065 b1 −1.393 −0.655−0.875 −0.159 a2 −0.636 −0.389 −0.219 0.262 b2 −1.018 −0.587 −0.514−0.170 a3 −0.451 −0.247 −0.350 −0.005 b3 0.211 0.128 −0.121 −0.252 a4−0.143 −0.047 −0.042 −0.043 b4 0.321 0.194 0.085 −0.071 a5 0 0 0 0 b5 00 0 0 a6 0 0 0 0 b6 0 0 0 0 a7 0 0 0 0 b7 0 0 0 0 a8 0 0 0 0 b8 0 0 0 0a9 0 0 0 0 b9 0 0 0 0 a10 0 0 0 0 b10 0 0 0 0 a11 0 0 0 0 b11 0 0 0 0a12 0 0 0 0 b12 0 0 0 0 a13 0 0 0 0 b13 0 0 0 0 a14 0 0 0 0 b14 0 0 0 0a15 0 0 0 0 b15 0 0 0 0 RSq 0.996 0.996 0.990 0.991 RMSE 0.021 0.0470.078 0.061Table 25 shows the values of the coefficients of the Fourier seriesexpansion (up to 15^(th) order) obtained when the power profilesdescribed in FIGS. 119 to 123 are best fitted to Fourier seriesexpansion via non-linear least square optimisation routines.

TABLE 26 Fourier Series Coefficients-Exemplary embodiments Coefficients# 1 # 2 # 3 # 4 # 5 # 6 C 168.296 369.426 −392.764 24.727 46.853 −83.250a1 171.234 288.170 −294.109 29.948 50.561 −85.924 b1 −273.020 −640.337694.809 −37.257 −73.531 136.391 a2 −123.956 −400.556 461.567 −10.869−29.150 60.878 b2 −255.061 −451.537 478.555 −41.846 −72.310 129.114 a3−227.309 −446.024 501.810 −33.584 −60.545 114.909 b3 −24.293 138.705−189.989 −12.626 −11.935 14.480 a4 −103.664 −40.397 18.166 −21.972−30.713 53.491 b4 131.984 320.561 −393.610 15.896 31.941 −65.781 a537.039 166.727 −234.450 1.169 6.725 −17.924 b5 104.599 104.297 −115.79217.540 26.782 −52.700 a6 63.445 86.909 −119.056 8.762 14.204 −31.065 b614.614 −55.880 98.644 4.689 4.874 −6.811 a7 24.044 −4.896 21.003 3.6864.991 −10.817 b7 −22.833 −44.530 77.014 −2.224 −3.994 11.065 a8 −2.251−13.916 34.396 0.258 0.229 1.692 b8 −13.756 −5.371 6.438 −1.406 −2.0166.015 a9 −4.019 −2.539 7.262 0 0 1.527 b9 −2.198 1.745 −9.661 0 0 0.959a10 −0.800 0 −0.785 0 0 0 b10 0.214 0 −2.831 0 0 0 a11 0 0 0 0 0 0 b11 00 0 0 0 0 a12 0 0 0 0 0 0 b12 0 0 0 0 0 0 a13 0 0 0 0 0 0 b13 0 0 0 0 00 a14 0 0 0 0 0 0 b14 0 0 0 0 0 0 a15 0 0 0 0 0 0 b15 0 0 0 0 0 0 RSq0.994 0.995 0.995 0.995 0.994 0.998 RMSE 0.039 0.049 0.056 0.046 0.0670.038Table 26 shows the values of the coefficients of the Fourier seriesexpansion (up to 15^(th) order) obtained when the power profilesdescribed in FIGS. 124 to 127 are best fitted to Fourier seriesexpansion via non-linear least square optimisation routines.

TABLE 27 Fourier Series Coefficients-Exemplary embodiments Coefficients# 7 # 8 # 9 # 10 # 11 # 12 C 58.457 39.751 −122.114 −251.936 −459.112−497.230 a1 56.670 43.870 −99.903 −233.067 −420.835 −434.644 b1 −95.096−62.002 212.063 422.837 771.200 845.729 a2 −45.579 −23.744 128.595225.195 413.877 480.153 b2 −82.605 −62.683 157.435 357.876 645.119673.003 a3 −71.978 −52.579 154.982 336.962 606.754 645.935 b3 −1.872−11.624 −37.489 −19.450 −42.362 −93.517 a4 −26.022 −27.669 23.262105.815 183.109 152.538 b4 41.524 27.952 −109.436 −220.519 −396.548−439.505 a5 13.238 6.058 −55.058 −92.151 −166.404 −203.356 b5 25.79124.423 −42.737 −129.674 −226.210 −215.240 a6 14.501 13.187 −33.856−90.981 −157.995 −159.694 b6 1.339 4.384 17.261 10.147 20.315 45.225 a73.533 4.605 0.167 −17.992 −29.510 −17.186 b7 −4.576 −3.961 17.567 42.01872.278 78.144 a8 −0.200 0.121 6.291 11.352 19.360 24.012 b8 −1.599−1.964 2.782 14.748 24.392 20.098 a9 0 0 1.789 5.987 9.681 8.948 b9 0 0−0.716 −0.718 −1.304 −3.406 a10 0 0 0 0.482 0.687 0.151 b10 0 0 0 −1.023−1.632 −1.711 a11 0 0 0 0 0 0 b11 0 0 0 0 0 0 a12 0 0 0 0 0 0 b12 0 0 00 0 0 a13 0 0 0 0 0 0 b13 0 0 0 0 0 0 a14 0 0 0 0 0 0 b14 0 0 0 0 0 0a15 0 0 0 0 0 0 b15 0 0 0 0 0 0 RSq 0.994 0.991 0.990 0.993 0.993 0.991RMSE 0.053 0.084 0.099 0.038 0.049 0.072Table 27 shows the values of the coefficients of the Fourier seriesexpansion (up to 15^(th) order) obtained when the power profilesdescribed in FIGS. 124 to 127 are best fitted to Fourier seriesexpansion via non-linear least square optimisation routines.

Section 26: Effect of Plus Power within the Optic Zone on the OpticalTransfer Function

FIGS. 109, 111 and 113 show the power profiles as a function ofhalf-chord diameter for some exemplary lens designs. The set of threedesigns illustrated in each of the FIGS. 109, 111 and 113 have about+3D, +6D, +10D power at the centre of half-chord that graduallydecreases to 0D at a certain given point on the half-chord diameter ofthe lens. In each of the FIGS. 109, 111 and 113, the point ofintersection of the power profile and the x-axis occurs at 0.5 mm(dashed black line), 0.75 mm (a solid grey line) and 1 mm (solid blackline) on the half-chord for the three different power profiles.

FIGS. 110, 112 and 114 show the modelled optical performance of theexemplary power profiles disclosed in FIGS. 109, 111 and 113,respectively. The modelled performance is gauged in terms of the realpart of the optical transfer function as a function of various spatialfrequencies, obtained. The optical transfer function portion describedin the equations disclosed in section 1 was used to gauge the opticalperformance of the profiles illustrated in these figures. Theperformance was modelled using a 4 mm pupil diameter. However, otherpupil diameters may also be used. The neural contrast sensitivityfunction is also plotted in the FIGS. 110, 112 and 114 as a function ofspatial frequencies to facilitate gauging the impact of the designedplus power in the centre of the lens on the optical transfer function.In the examples illustrated in these figures, the drop in the modulationof the real part of the optical transfer function as a function ofspatial frequencies was compared with neural contrast sensitivityfunction to gauge the impact on vision. As shown in FIGS. 110, 112 and114, the addition of plus power varying from +3D to +10D if limited to0.5 mm of the half-chord diameter of the optic zone of the lens, thedrop in the contrast/modulation transfer for mid spatial frequency (i.e.15 cycles/degree) is 0.8. In contrast, when the addition of plus varyingfrom +3D to +10D is greater than 0.5 mm or 0.75 mm of the half-chord,then drop in the contrast/modulation transfer for mid spatialfrequencies (i.e. cycles/degree) is 0.6. Accordingly, in someembodiments, power profiles may be optimised to have less impact on theoptical transfer function by selecting varying degrees of plus powerranging from +3D to +10D in zone widths ranging from 0.25 mm to 1 mm ofthe half-chord of the lens. Such embodiments may include other featurediscussed in the present disclosure.

Certain embodiments may have power profiles that include appropriatecombinations of the power profiles disclosed herein, for example, thepower profiles described in sections 22 (i), section 22 (ii) or section22 (iii). In some combinations, the power profile may also have varyingdegrees of additional plus power ranging from +3 D to +10 D relative tothe prescription power within an appropriate range of the half-chord ofthe optic zone. For example, in some embodiments, the appropriate rangeon the half-chord of the optic zone may be one of the following: 0 to0.25 mm, 0 to 0.5 mm or 0 to 0.75 mm. Such combinations may provideacceptable vision and/or minimal ghosting for at least a subset of apopulation.

Some embodiments may be directed to lenses, methods and/or devicescomprising: an optical axis; a power profile with transitions betweenmaxima and its adjacent minima, wherein the maxima is within 0.2 mm, andthe adjacent minima is within at least 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9or 1 mm, distance from the centre of an optic zone of the lens, thetransition zone between the maxima and its adjacent minima can becontinuous, substantially continuous, smooth, substantially smooth,discontinuous or certain combinations thereof; the amplitude of thetransition zone between the maxima and its adjacent minima is at least+2 D, +2.25 D, +2.5 D, +2.75 D, +3 D, +3.25 D, +3.5 D, +4 D, +4.5 D, +5D, +5.5 D, +6 D, +6.5 D, +7 D, +7.5 D, +8 D, +8.5 D, +9 D, +9.5 D or +10D.

Other exemplary embodiments are described in the following sets ofexamples A to X:

Example Set A

(A1) A lens for an eye, the lens having an optical axis and anaberration profile about its optical axis, the aberration profile:having a focal distance; and including higher order aberrations havingat least one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0), wherein the aberrationprofile provides, for a model eye with no aberrations, or substantiallyno aberrations, and an on-axis length equal to, or substantial equal to,the focal distance: a retinal image quality (RIQ) with a through focusslope that degrades in a direction of eye growth; and a RIQ of at least0.3 wherein the RIQ is visual Strehl Ratio measured substantially alongthe optical axis for at least one pupil diameter in the range 3 mm to 6mm, over a spatial frequency range of 0 to 30 cycles/degree inclusiveand at a wavelength selected from within the range 540 nm to 590 nminclusive.

(A2) A lens for an eye, the lens having an optical axis and anaberration profile about its optical axis, the aberration profile:having a focal distance; and including higher order aberrations havingat least one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0), wherein the aberrationprofile provides, for a model eye with no aberrations and an on-axislength equal to the focal distance: a retinal image quality (RIQ) with athrough focus slope that degrades in a direction of eye growth; and aRIQ of at least 0.3 wherein the RIQ is visual Strehl Ratio measuredsubstantially along the optical axis for at least one pupil diameter inthe range 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(A3) A lens for an eye, the lens having an optical axis, a focaldistance and being characterised by: an aberration profile about thelens's optical axis, the aberration profile: including higher orderaberrations having at least one of a primary spherical aberrationcomponent C(4,0) and a secondary spherical aberration component C(6,0),wherein the aberration profile provides, for a model eye with noaberrations, or substantially no, aberrations, and an on-axis lengthequal to, or substantial equal to, the focal distance: a retinal imagequality (RIQ) with a through focus slope that degrades in a direction ofeye growth; and a RIQ of at least 0.3, wherein the RIQ is visual StrehlRatio measured substantially along the optical axis for at least onepupil diameter in the range 3 mm to 6 mm, over a spatial frequency rangeof 0 to 30 cycles/degree inclusive and at a wavelength selected fromwithin the range 540 nm to 590 nm inclusive.

(A4) A lens for an eye, the lens having at least one optical axis and atleast one optical profile substantially about the at least one opticalaxis, the optical profile: having at least one focal distance; andincluding one or more higher order aberrations, wherein the profileprovides, for a model eye with substantially no aberrations an on-axislength equal to, or substantially equal to, the desired focal distance;a retinal image quality (RIQ) with a through focus slope that improvesin a direction of eye growth; and a RIQ of at least 0.3; wherein the RIQis measured substantially along the optical axis for at least one pupildiameter in the range 3 mm to 6 mm, over a spatial frequency range of 0to 30 cycles/degree inclusive and at a wavelength selected from withinthe range 540 nm to 590 nm inclusive.

(A5) A lens for an eye, the lens having an optical axis and anaberration profile about its optical axis, the aberration profile:having a focal distance; and including higher order aberrations havingat least one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0), wherein the aberrationprofile provides, for a model eye with no aberrations, or substantiallyno, aberrations, and an on-axis length equal to, or substantial equalto, the focal distance: a retinal image quality (RIQ) with a throughfocus slope that improves in a direction of eye growth; and a RIQ of atleast 0.3, wherein the RIQ is visual Strehl Ratio measured substantiallyalong the optical axis for at least one pupil diameter in the range 3 mmto 6 mm, over a spatial frequency range of 0 to 30 cycles/degreeinclusive and at a wavelength selected from within the range 540 nm to590 nm inclusive.

(A6) A lens for an eye, the lens having an optical axis and anaberration profile about its optical axis, the aberration profile:having a focal distance; and including higher order aberrations havingat least one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0), wherein the aberrationprofile provides, for a model eye with no aberrations and an on-axislength equal to the focal distance: a retinal image quality (RIQ) with athrough focus slope that improves in a direction of eye growth; and aRIQ of at least 0.3, wherein the RIQ is visual Strehl Ratio measuredsubstantially along the optical axis for at least one pupil diameter inthe range 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(A7) A lens for an eye, the lens having an optical axis, a focaldistance and being characterised by: an aberration profile about thelens's optical axis, the aberration profile: including higher orderaberrations having at least one of a primary spherical aberrationcomponent C(4,0) and a secondary spherical aberration component C(6,0),wherein the aberration profile provides, for a model eye with noaberrations, or substantially no, aberrations, and an on-axis lengthequal to, or substantial equal to, the focal distance: a retinal imagequality (RIQ) with a through focus slope that improves in a direction ofeye growth; and a RIQ of at least 0.3, wherein the RIQ is visual StrehlRatio measured substantially along the optical axis for at least onepupil diameter in the range 3 mm to 6 mm, over a spatial frequency rangeof 0 to 30 cycles/degree inclusive and at a wavelength selected fromwithin the range 540 nm to 590 nm inclusive.

(A8) A lens for an eye, the lens having at least one optical axis and atleast one optical profile substantially about the at least one opticalaxis, the optical profile: having at least one focal distance; andincluding one or more higher order aberrations, wherein the profileprovides, for a model eye with substantially no aberrations an on-axislength equal to, or substantially equal to, the desired focal distance;a retinal image quality (RIQ) with a through focus slope that improvesin a direction of eye growth; and a RIQ of at least 0.3; wherein the RIQis measured substantially along the optical axis for at least one pupildiameter in the range 3 mm to 6 mm, over a spatial frequency range of 0to 30 cycles/degree inclusive and at a wavelength selected from withinthe range 540 nm to 590 nm inclusive.

(A9) The lens of one or more of the above A examples, wherein the focaldistance is a prescription focal distance for a myopic eye and whereinthe focal distance differs from the focal distance for a C(2,0) Zernikecoefficient of the aberration profile.

(A10) The lens of one or more of the above A examples, wherein the focaldistance is a prescription focal distance for a hyperopic eye andwherein the focal distance differs from the focal distance for a C(2,0)Zernike coefficient of the aberration profile.

(A11) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least two spherical aberration termsselected from the group C(4,0) to C(20,0).

(A12) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least three spherical aberrationterms selected from the group C(4,0) to C(20,0).

(A13) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least four spherical aberrationterms selected from the group C(4,0) to C(20,0).

(A14) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least five spherical aberrationterms selected from the group C(4,0) to C(20,0).

(A15) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least six spherical aberration termsselected from the group C(4,0) to C(20,0).

(A16) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least seven spherical aberrationterms selected from the group C(4,0) to C(20,0).

(A17) The lens of one or more of the above A examples, wherein themagnitude of higher order aberrations included is at least 0.01 μm overa 4 mm, 5 mm or 6 mm pupil diameter.

(A18) The lens of one or more of the above A examples, wherein themagnitude of higher order aberrations included is at least 0.02 μm overa 4 mm, 5 mm or 6 mm pupil diameter.

(A19) The lens of one or more of the above A examples, wherein themagnitude of higher order aberrations included is at least 0.03 μm overa 4 mm, 5 mm or 6 mm pupil diameter.

(A20) The lens of one or more of the above A examples, wherein themagnitude of higher order aberrations included is at least 0.04 μm overa 4 mm, 5 mm or 6 mm pupil diameter.

(A21) The lens of one or more of the above A examples, wherein themagnitude of higher order aberrations included is at least 0.05 μm overa 4 mm, 5 mm or 6 mm pupil diameter.

(A22) The lens of one or more of the above A examples, wherein themagnitude of higher order aberrations included is at least 0.01 μm, 0.02μm, 0.03 μm or 0.04 μm over a 3 mm pupil diameter.

(A23) The lens of one or more of the above A examples, wherein theaverage slope over a horizontal field of at least −20° to +20° degradesin a direction of eye growth.

(A24) The lens of one or more of the above A examples, wherein theaverage slope over a vertical field of at least −20° to +20° degrades inthe direction of eye growth.

(A25) The lens of one or more of the above A examples, wherein the slopefor a substantial portion of the field angles over a horizontal field ofat least −20° to +20° degrades in the direction of eye growth.

(A26) The lens of one or more of the above A examples, wherein the slopefor a substantial portion of the field angles over a vertical field ofat least −20° to +20° degrades in the direction of eye growth.

(A27) The lens of one or more of the above A examples, wherein theaberration profile provides a RIQ of at least 0.3 at the focal lengthfor a substantial portion of the pupil diameters in the range 3 mm to 6mm.

(A28) The lens of one or more of the above A examples, wherein theaberration profile provides a RIQ of at least 0.3 at the focal lengthfor a substantial portion of pupil diameters in the range 4 mm to 5 mm.

(A29) The lens of one or more of the above A examples, wherein thethrough focus slope averaged over the horizontal field of at least −20°to +20° degrades in the direction of eye growth.

(A30) The lens of one or more of the above A examples, wherein thethrough focus slope averaged over the vertical field of at least −20° to+20° degrades in the direction of eye growth.

(A31) The lens of one or more of the above A examples, wherein thethrough focus slope for a substantial portion of the field angles overthe horizontal field of at least −20° to +20° degrades in the directionof eye growth.

(A32) The lens of one or more of the above A examples, wherein thethrough focus slope for a substantial portion of the field angles overthe vertical field of at least −20° to +20° degrades in the direction ofeye growth.

(A33) The lens of one or more of the above A examples, wherein theaberration profile provides a RIQ with a through focus slope thatdegrades in the direction of eye growth when primary astigmatism isadded to the aberration profile.

(A34) The lens of one or more of the above A examples, wherein theaberration profile provides a RIQ with a through focus slope thatimproves in the direction of eye growth when primary astigmatism isadded to the aberration profile.

(A35) The lens of one or more of the above A examples, wherein theaberration profile provides a RIQ with a through focus slope thatdegrades in the direction of eye growth when secondary astigmatism isadded to the aberration profile.

(A36) The lens of one or more of the above A examples, wherein theaberration profile provides a RIQ with a through focus slope thatimproves in the direction of eye growth when secondary astigmatism isadded to the aberration profile.

(A37) The lens of one or more of the above A examples, wherein the RIQis, or is characterised by:

${R\; I\; Q} = \frac{\begin{matrix}{\int{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,y} )}*}}} \\( {{real}( ( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,y} )}*}}} \\( ( ( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

-   -   Wherein:    -   Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;    -   CSF(x, y) denotes the contrast sensitivity function,    -   CSF(F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1),    -   Where f specifies the tested spatial frequency, in the range of        F_(min) to F_(max);    -   FT denotes a 2D Fourier transform, for example, a 2D fast        Fourier transform;    -   A(ρ,θ) denotes the pupil amplitude function across the pupil        diameter;    -   W(ρ,θ) denotes wavefront of the test case measured for i=1 to        20;

${W( {\rho,\theta} )} = {\sum\limits_{i = 1}^{k}{a_{i}{Z_{i}( {\rho,\theta} )}}}$

-   -   Wdiff(ρ, θ) denotes wavefront of the diffraction limited case;    -   ρ and θ are normalised polar coordinates, where ρ represents the        radial coordinate and θ represents the angular coordinate or        azimuth; and    -   λ denotes wavelength.

(A38) The lens of one or more of the above A examples, wherein the RIQis, or is characterised by:

${R\; I\; Q} = \frac{\begin{matrix}{\int{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,y} )}*}}} \\( {{real}( ( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,y} )}*}}} \\( ( ( {F\; {T( {{F\; T\{ {{A( {\rho,\theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

-   -   Wherein:    -   Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;    -   CSF(x, y) denotes the contrast sensitivity function,    -   CSF (F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1),    -   Where f specifies the tested spatial frequency, in the range of        F_(min) to F_(max);    -   FT denotes a 2D Fourier transform, for example, a 2D fast        Fourier transform;    -   A(ρ,θ) denotes the pupil amplitude function across the pupil        diameter;    -   W(ρ,θ) denotes wavefront of the test case measured for i=1 to k;    -   where k is a positive integer;

${W( {\rho,\theta} )} = {\sum\limits_{i = 1}^{k}{a_{i}{Z_{i}( {\rho,\theta} )}}}$

-   -   Wdiff(ρ, θ) denotes wavefront of the diffraction limited case;    -   ρ and θ are normalised polar coordinates, where ρ represents the        radial coordinate and θ represents the angular coordinate or        azimuth; and    -   λ denotes wavelength.

(A39) A lens including an optical axis and an aberration profile aboutthe optical axis that provides: a focal distance for a C(2,0) Zernikecoefficient term; a peak visual Strehl Ratio (‘first visual StrehlRatio’) within a through focus range, and a visual Strehl Ratio thatremains at or above a second visual Strehl Ratio over the through focusrange that includes said focal distance, wherein the visual Strehl Ratiois measured for a model eye with no, or substantially no, aberration andis measured along the optical axis for at least one pupil diameter inthe range 3 mm to 5 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive, at a wavelength selected from within the range540 nm to 590 nm inclusive, and wherein the first visual Strehl Ratio isat least 0.35, the second visual Strehl Ratio is at least 0.1 and thethrough focus range is at least 1.8 Dioptres.

(A40) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio is at least 0.28 or 0.3.

(A41) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio is at least 0.4.

(A42) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio is at least 0.5.

(A43) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio is at least 0.6.

(A44) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio is at least 0.7.

(A45) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio is at least 0.8.

(A46) The lens of one or more of the above A examples, wherein thesecond visual Strehl Ratio is at least 0.08, 0.1, 0.12, 0.14, 0.16, 0.18or 0.2.

(A47) The lens of one or more of the above A examples, wherein thethrough focus range is at least 1.8 Dioptres.

(A48) The lens of one or more of the above A examples, wherein thethrough focus range is at least 1.9 Dioptres.

(A49) The lens of one or more of the above A examples, wherein thethrough focus range is at least 2 Dioptres.

(A50) The lens of one or more of the above A examples, wherein thethrough focus range is at least 2.1 Dioptres.

(A51) The lens of one or more of the above A examples, wherein thethrough focus range is at least 2.25 Dioptres.

(A52) The lens of one or more of the above A examples, wherein thethrough focus range is at least 2.5 Dioptres.

(A53) The lens of one or more of the above A examples, wherein the lenshas a prescription focal distance located within 0.75 Dioptres of an endof the through focus range.

(A54) The lens of one or more of the above A examples, wherein the lenshas a prescription focal distance located within 0.5 Dioptres of an endof the through focus range.

(A55) The lens of one or more of the above A examples, wherein the lenshas a prescription focal distance located within 0.3 Dioptres of an endof the through focus range.

(A56) The lens of one or more of the above A examples, wherein the lenshas a prescription focal distance located within 0.25 Dioptres of an endof the through focus range.

(A57) The lens of one or more of the above A examples, wherein the endof the through focus range is the negative power end.

(A58) The lens of one or more of the above A examples, wherein the endof the through focus range is the positive power end.

(A59) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio remains at or above the second visual Strehl Ratioover the through focus range and over a range of pupil diameters of atleast 1 mm.

(A60) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio remains at or above the second visual Strehl Ratioover the through focus range and over a range of pupil diameters of atleast 1.5 mm.

(A61) The lens of one or more of the above A examples, wherein the firstvisual Strehl Ratio remains at or above the second visual Strehl Ratioover the through focus range and over a range of pupil diameters of atleast 2 mm.

(A62) The lens of one or more of the above A examples, wherein thecombination of higher order aberrations includes at least one of primaryspherical aberration and secondary spherical aberration.

(A63) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least two spherical aberration termsselected from the group C(4,0) to C(20,0).

(A64) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least three spherical aberrationterms selected from the group C(4,0) to C(20,0).

(A65) The lens of one or more of the above A examples, wherein thehigher order aberrations include at least five spherical aberrationterms selected from the group C(4,0) to C(20,0).

(A66) The lens of one or more of the above A examples, wherein theaberration profile is substantially described using only sphericalaberration Zernike coefficients C(4,0) to C(20,0).

(A67) The lens of one or more of the above A examples, wherein the RIQfor every field angle over a horizontal field of at least −10° to +10°is at least 0.2, 0.25, 0.3, 0.35 or 0.4.

(A68) The lens of one or more of the above A examples, wherein the RIQfor every field angle over a horizontal field of at least −20° to +20°is at least 0.2, 0.25, 0.3, 0.35 or 0.4.

(A69) The lens of one or more of the above A examples, wherein the RIQfor every field angle over a horizontal field of at least −30° to +30°is at least 0.2, 0.25, 0.3, 0.35 or 0.4.

(A70) The lens of one or more of the above A examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(A71) The lens of one or more of the above A examples, wherein theaberration profile is an aberration pattern.

(A72) A method for a presbyopic eye, the method comprising identifyingat least one wavefront aberration profile for the eye, the at least onewavefront aberration profile including at least two spherical aberrationterms, wherein the prescription focal distance of the lens is determinedtaking into account said at least one spherical aberration and whereinthe prescription focal distance of the lens is at least +0.25D relativeto a focal distance for a C(2,0) Zernike coefficient term of the atleast one wavefront aberration and producing one or more of thefollowing: a device, lens and corneal profile for the eye to affect saidat least one wavefront aberration profile.

(A73) A method for a myopic or emmetropic eye, the method comprisingforming an aberration for the eye and applying or prescribing theaberration profile, the aberration profile: having a focal distance; andincluding at least one of a primary spherical aberration componentC(4,0) and a secondary spherical aberration component C(6,0), whereinthe aberration profile provides, for the eye: a retinal image quality(RIQ) with a through focus slope that degrades in a direction of eyegrowth; and a RIQ of at least 0.3; wherein said RIQ is visual StrehlRatio measured along the optical axis for at least one pupil diameter inthe range 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(A74) A method for a hyperopic eye, the method comprising forming anaberration for the eye and applying or prescribing the aberrationprofile, the aberration profile: having a focal distance; and includingat least one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0), wherein the aberrationprofile provides, for the eye: a retinal image quality (RIQ) with athrough focus slope that improves in a direction of eye growth; and aRIQ of at least 0.3; wherein said RIQ is visual Strehl Ratio measuredalong the optical axis for at least one pupil diameter in the range 3 mmto 6 mm, over a spatial frequency range of 0 to 30 cycles/degreeinclusive and at a wavelength selected from within the range 540 nm to590 nm inclusive.

(A75) The method of one or more of the above A method examples, whereinapplying or prescribing the aberration profile comprises providing alens, the lens having an aberration profile including at least twospherical aberration terms selected from the group C(4,0) to C(20,0).

(A76) The method of one or more of the above A method examples, whereinapplying or prescribing the aberration profile comprises providing alens, the lens having an aberration profile including at least threespherical aberration terms selected from the group C(4,0) to C(20,0).

(A77) The method of one or more of the above A method examples, whereinapplying or prescribing the aberration profile comprises providing alens, the lens having an aberration profile including at least fivespherical aberration terms selected from the group C(4,0) to C(20,0).

(A78) A method for a myopic eye, the method comprising identifying awavefront aberration profile for the eye and applying or prescribing theaberration profile, the wavefront aberration profile including at leasttwo spherical aberration terms, wherein the prescription focal distanceof the lens is determined taking into account said spherical aberrationand wherein the prescription focal distance is at least +0.1D relativeto a focal distance for a C(2,0) Zernike coefficient term of thewavefront aberration profile and wherein the wavefront aberrationprofile provides a degrading retinal image quality in the directionposterior to the retina.

(A79) A method for a hyperopic eye, the method comprising identifying awavefront aberration profile for the eye and applying or prescribing theaberration profile, the wavefront aberration profile including at leasttwo spherical aberration terms, wherein the prescription focal distanceof the lens is determined taking into account said spherical aberrationand wherein the prescription focal distance is at least +0.1D relativeto a focal distance for a C(2,0) Zernike coefficient term of thewavefront aberration profile and wherein the wavefront aberrationprofile provides a improving retinal image quality in the directionposterior to the retina.

(A80) The method of one or more of the above A method examples, whereinthe prescription focal distance is at least +0.1D relative to a focaldistance for a C(2,0) Zernike coefficient term of the wavefrontaberration profile.

(A81) A method for a hyperopic eye, the method comprising identifying awavefront aberration profile for the eye and applying or prescribing theaberration profile, the wavefront aberration profile including at leasttwo spherical aberration terms, wherein the prescription focal distanceof the lens is determined taking into account said spherical aberrationand wherein at the prescription focal distance the wavefront aberrationprofile provides an improving retinal image quality in the directionposterior to the retina.

(A82) The method of one or more of the above A method examples, whereinthe lens does not substantially reduce the amount of light passingthrough the lens.

(A83) The method of one or more of the above A method examples, whereinthe aberration profile is an aberration pattern.

Example Set B

(B1) A multifocal lens comprising: an optical axis; an effective nearadditional power of at least 1D; the optical properties of themultifocal lens are configured with an aberration profile associatedwith the optical axis; the aberration profile is comprised of a defocusterm and at least two spherical aberration terms; and the multifocallens is configured to provide a visual performance over intermediate andfar distances that is at least substantially equivalent to the visualperformance of a correctly prescribed single-vision lens at the farvisual distance; and is configured to provide minimal ghosting at far,intermediate and near distances.

(B2) The multifocal lens of one or more of the above B examples, whereinthe lens is configured to provide near visual acuity of at least 6/6 inindividuals that can achieve 6/6 visual acuity.

(B3) The multifocal lens of one or more of the above B examples, whereinthe lens is configured to provide at least acceptable visual performanceat near distances.

(B4) A multifocal lens comprising: an optical axis; an effective nearadditional power of at least 0.75D; the optical properties of themultifocal lens are configured or described based at least in part on anaberration profile associated with the optical axis; the aberrationprofile is comprised of a defocus term and at least two sphericalaberration terms; and the multifocal lens is configured to provide avisual performance, along a range of substantially continuous nearvisual distances, wherein the visual performance of the multifocal lensis at least substantially equivalent to the visual performance of acorrectly prescribed single-vision lens at the far visual distance, themultifocal lens is configured to provide a visual performance, along arange of substantially continuous intermediate and far visual distances,wherein the visual performance of the multifocal lens is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance.

(B5) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured or described based atleast in part on an aberration profile associated with the optical axis;wherein the aberration profile is comprised of a defocus term and atleast two spherical aberration terms; and wherein the multifocal lens isconfigured to provide a visual performance, along a range ofsubstantially continuous visual distances, including near, intermediateand far distances, wherein the visual performance of the multifocal lensis at least substantially equivalent to the visual performance of acorrectly prescribed single-vision lens at the far visual distance.

(B6) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured or described based atleast in part on an aberration profile associated with the optical axis;the aberration profile is comprised of a defocus term and at least twospherical aberration terms; and the multifocal lens is configured toprovide a visual performance, along substantially continuous visualdistances, including substantially near distances, substantiallyintermediate distances, and substantially far distances, wherein thevisual performance of the multifocal lens is at least substantiallyequivalent to the visual performance of an appropriately prescribedsingle-vision lens at the far visual distance.

(B7) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured or described based onan aberration profile associated with the optical axis; the aberrationprofile is comprised of a defocus term and at least two aberrationterms; and the multifocal lens is configured to provide a visualperformance, along a range of visual distances, including near,intermediate and far distances, wherein the visual performance of thelens is at least equivalent to the visual performance of a single-visionlens at the far visual distance.

(B8) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured or described based onan aberration profile associated with the optical axis; wherein theaberration profile is comprised of a defocus term and at least twoaberration terms; and wherein the multifocal lens is configured toprovide a visual performance, along a range of visual distances,including near, intermediate and far distances, wherein the visualperformance of the lens is at least equivalent to the visual performanceof a single-vision lens at the far visual distance.

(B9) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured or described based atleast in part on an aberration profile associated with the optical axis;the aberration profile is comprised of a defocus term, at least twospherical aberration term and at least one asymmetric term; and themultifocal lens is configured to provide a visual performance, along arange of substantially continuous visual distances, including near,intermediate and far distances, wherein the visual performance of themultifocal lens is at least substantially equivalent to the visualperformance of a correctly prescribed single-vision lens at the farvisual distance.

(B10) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured or described based onan aberration profile associated with the optical axis; the aberrationprofile is comprised of a defocus term and at least two sphericalaberration terms; and the multifocal lens is configured to provide avisual performance over intermediate and far distances that is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance; and isconfigured to provide minimal ghosting at far, intermediate and neardistances.

(B11) A multifocal lens for correction of presbyopia comprising: anoptical axis; the optical properties of the multifocal lens areconfigured or described based on an aberration profile associated withthe optical axis; the aberration profile is comprised of a defocusterms, at least two spherical aberration terms and at least oneasymmetric aberration term; and the multifocal lens is configured toprovide a visual performance over intermediate and far distances that isat least substantially equivalent to the visual performance of acorrectly prescribed single-vision lens at the far visual distance; andis configured to provide minimal ghosting at far, intermediate and neardistances.

(B12) A multifocal lens for correction of presbyopia comprising: anoptical axis; combinations of one more areas of different focal powers;and the optical properties of the multifocal lens is configured toprovide a visual performance for a presbyopic eye over intermediate andfar distances that is at least substantially equivalent to the visualperformance of a correctly prescribed single-vision lens at the farvisual distance; and is configured to provide minimal ghosting at far,intermediate and near distances.

(B13) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens is characterised at least in part onan aberration profile associated with the optical axis; the aberrationprofile is comprised of a defocus term and at least two sphericalaberration term; and the multifocal lens is configured to provide avisual performance over intermediate and far distances that is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance; and isconfigured to provide minimal ghosting at far, intermediate and neardistances.

(B14) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured or described based atleast in part on an aberration profile associated with the optical axis;the aberration profile is comprised of a defocus term and at least twospherical aberration terms; and the multifocal lens is configured toprovide a visual performance over intermediate and far distances that isat least substantially equivalent to the visual performance of aprescribed single-vision lens at the far visual distance; and isconfigured to provide minimal ghosting at far, intermediate and neardistances.

(B15) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured based on an aberrationprofile associated with the optical axis of the lens; the aberrationprofile is comprised of a defocus term and at least two sphericalaberration terms; and the multifocal lens is configured to provide avisual performance over intermediate and far distances that is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance; and isconfigured to provide minimal ghosting at far, intermediate and neardistances.

(B16) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens being characterised based on anaberration profile associated with the optical axis of the lens; theaberration profile is comprised of a defocus term and at least twospherical aberration terms; and the multifocal lens is configured toprovide a visual performance over intermediate and far distances that isat least substantially equivalent to the visual performance of aeffectively prescribed single-vision lens at the far visual distance;and is configured to provide minimal ghosting at far, intermediate andnear distances.

(B17) The multifocal lens of one or more of the above B examples,wherein the lens does not substantially reduce the amount of lightpassing through the lens.

(B18) The multifocal lens of one or more of the above B examples,wherein the amount of light passing through the lens is at least 80%,85%, 90%, 95% or 99%.

(B19) The multifocal lens of one or more of the above B examples,wherein the single-vision lens is one or more of the following:prescribed, appropriately prescribed, correctly prescribed andeffectively prescribed.

(B20) The multifocal lens of one or more of the above B examples,wherein the single-vision lens is a lens with a substantially constantpower across a substantial portion of an optic zone of the single-visionlens.

(B21) The multifocal lens of one or more of the above B examples,wherein the single-vision lens is a lens with a constant power across aportion of an optic zone of the single-vision lens.

(B22) The multifocal lens of one or more of the above B examples,wherein the single-vision lens is a lens with a substantially constantpower across a portion of one or more optic zones of the single-visionlens.

(B23) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is used for a presbyopic eye.

(B24) The multifocal lens of one or more of the above B examples,wherein the lens is configured for a presbyopic eye.

(B25) The multifocal lens of one or more of the above B examples,wherein the lens is configured to optically correct or substantiallycorrect presbyopia.

(B26) The multifocal lens of one or more of the above B examples,wherein the lens is configured to mitigate or substantially mitigate theoptical consequences of presbyopia.

(B27) The multifocal lens of one or more of the above B examples,wherein the lens is configured to alter or substantially alter apresbyopic condition to a non-presbyopic condition.

(B28) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is used for at least correcting a presbyopiceye condition and when used provides an appropriate correction to adjustthe vision of the user towards substantially normal non-presbyopicvision.

(B29) The multifocal lens of one or more of the above B examples,wherein normal vision is 6/6 or better.

(B30) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further characterised by minimal,substantially no or no, ghosting at near, intermediate and fardistances.

(B31) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further characterised by minimal,substantially no or no, ghosting at near distances, intermediatedistances and far distances.

(B32) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide minimal,substantially no or no, ghosting at near, intermediate and fardistances.

(B33) The multifocal lens of one or more of the above B examples,wherein the minimal ghosting is a lack of an undesired secondary imageappearing at the image plane of the optical system.

(B34) The multifocal lens of one or more of the above B examples,wherein the minimal ghosting is a lack of an undesired secondary imageappearing on the retina of the eye.

(B35) The multifocal lens of one or more of the above B examples,wherein the minimal ghosting is a lack of an undesired double imageappearing on the retina of the eye.

(B36) The multifocal lens of one or more of the above B examples,wherein the minimal ghosting is a lack of false out-of-focus imageappearing along side of the primary image in an optical system.

(B37) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide asufficient lack of ghosting in a portion of near, intermediate and fardistances.

(B38) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide asufficient lack of ghosting at near distances, intermediate distancesand far distances.

(B39) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide asufficient lack of ghosting in a portion of two or more of thefollowing: near, intermediate and far distances.

(B40) The multifocal lens of one or more of the above B examples,wherein lack of ghosting is lack of undesired image appearing at theimage plane of the optical system.

(B41) The multifocal lens of one or more of the above B examples,wherein lack of ghosting is a lack of false out of focus imagesappearing along side of the primary image in an optical system.

(B42) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide asufficient lack of ghosting in a portion of two or more of thefollowing: near distances, intermediate distances and far distances.

(B43) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide the RIQ ofat least 0.1, 0.13, 0.17, 0.2, 0.225, or 0.25 in the near distancerange, the RIQ of at least 0.27, 0.3, 0.33, 0.35, 0.37 or 0.4 in theintermediate distance range and the RIQ of at least 0.35, 0.37, 0.4,0.42, 0.45, 0.47, or 0.5 in the far distance range.

(B44) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide the RIQ ofat least 0.1 in the near distance range, the RIQ of at least 0.2 in theintermediate distance range and the RIQ of at least 0.3 in the fardistance range.

(B45) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide two or moreof the following: the RIQ of at least 0.1, 0.13, 0.17, 0.2, 0.225, or0.25 in the near distance range, the RIQ of at least 0.27, 0.3, 0.33,0.35, 0.37 or 0.4 in the intermediate distance range and the RIQ of atleast 0.35, 0.37, 0.4, 0.42, 0.45, 0.47, or 0.5 in the far distancerange.

(B46) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is further configured to provide two or moreof the following: the RIQ of at least 0.1 in the near distance range,the RIQ of at least 0.2 in the intermediate distance range and the RIQof at least 0.3 in the far distance range.

(B47) The multifocal lens of one or more of the above B examples,wherein the RIQs are selected in the near, intermediate and far distanceranges such that the multifocal lens is configured to provide minimal,or no, ghosting in near, intermediate and far distances.

(B48) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is configured to substantially eliminate, orsubstantially reduce, ghosting at near, intermediate and far distances.

(B49) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is configured to substantially eliminate, orsubstantially reduce, ghosting at near distances, intermediate distancesand far distances.

(B50) The multifocal lens of one or more of the above B examples,wherein near distance is the range of 33 cm to 50 cm or 40 cm to 50 cm;intermediate distance is the range of 50 cm to 100 cm, 50 cm to 80 cm or50 cm to 70 cm; and far distance is the range of 100 cm or greater, 80cm or greater or 70 cm or greater.

(B51) The multifocal lens of one or more of the above B examples,wherein near distance is the range of 33 cm to 50 cm or 40 cm to 50 cm;intermediate distance is the range of 50 cm to 100 cm, 50 cm to 80 cm or50 cm to 70 cm; and far distance is the range of 100 cm or greater, 80cm or greater or 70 cm or greater and the near, intermediate and fardistances are determined by the distance from the object being focusedon.

(B52) The multifocal lens of one or more of the above B examples,wherein near distance is the range of 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm; and far distance is the rangeof 100 cm or greater.

(B53) The multifocal lens of one or more of the above B examples,wherein near distance is the range of 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm; and far distance is the rangeof 100 cm or greater and the near, intermediate and far distances aredetermined by the distance from the object being focused on.

(B54) The multifocal lens of one or more of the above B examples,wherein near distance is the range of 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm; and far distance is the rangeof 100 cm to optical infinity.

(B55) The multifocal lens of one or more of the above B examples,wherein near distance is the range of 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm; and far distance is the rangeof 100 cm to optical infinity and the near, intermediate and fardistances are determined by the distance from the object being focusedon.

(B56) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is configured to minimise, or reduce,ghosting at near, intermediate and far distances when used on an eye.

(B57) The multifocal lens of one or more of the above B examples,wherein the multifocal lens is configured to minimise, or reduce,ghosting at near distances, intermediate distances and far distanceswhen used on an eye.

(B58) The multifocal lens of one or more of the above B examples,wherein the range of substantially continuous distances is continuous.

(B59) The multifocal lens of one or more of the above B examples,wherein the range of substantially continuous distances is continuousand goes from 40 cm to optical infinity.

(B60) The multifocal lens of one or more of the above B examples,wherein the range of substantially continuous distances is from 33 cm tooptical infinity.

(B61) The multifocal lens of one or more of the above B examples,wherein the lens is configured such that at least 40%, 50%, 60% or 70%of a randomly selected group of 15 affected individuals in the neardistances, intermediate distances and far distances perceive minimal, orno, ghosting at near distances, intermediate distances and fardistances.

(B62) The multifocal lens of one or more of the above B examples,wherein the lens is configured such that at least 60%, 70%, 80% or 90%of a randomly selected group of 15 affected individuals in theintermediate distances and far distances perceive minimal, or no,ghosting at intermediate distances and far distances.

(B63) The multifocal lens of one or more of the above B examples,wherein the single vision lens provides a visual acuity for the user ofone or more of the following: at least 20/20, at least 20/30, at least20/40, at least about 20/20, at least about 20/30 and at least about20/40, at far visual distances.

(B64) The multifocal lens of one or more of the above B examples,wherein the aberration profile is comprised of a defocus term and atleast two, two or more, three, three or more, four, four or more, five,five or more, six, six or more, seven, seven or more, eight, eight ormore, nine, nine or more, ten, or ten or more spherical aberrationterms.

(B65) The multifocal lens of one or more of the above B examples,wherein the aberration profile is comprised of a defocus term and atleast two, three, four, five, six, seven, eight, nine, or at least tenspherical aberration terms.

(B66) The multifocal lens of one or more of the above B examples,wherein the aberration profile is comprised of a defocus term andspherical aberration terms between C(4,0) and C(6,0), C(4,0) and C(8,0),C(4,0) and C(10,0), C(4,0) and C(12,0), C(4,0) and C(14,0), C(4,0) andC(16,0), C(4,0) and C(18,0), or C(4,0) and C(20,0).

(B67) The multifocal lens of one or more of the above B examples,wherein the single vision lens provides a visual acuity that is thebest-corrected visual acuity.

(B68) The multifocal lens of one or more of the above B examples,wherein the best-corrected visual acuity is a visual acuity that cannotbe substantially improved by further manipulating the power of thesingle vision lens.

(B69) The multifocal lens of one or more of the above B examples,wherein the lens has two optical surfaces.

(B70) The multifocal lens of one or more of the above B examples,wherein the least one aberration profile is along the optical axis ofthe lens.

(B71) The multifocal lens of one or more of the above B examples,wherein the lens has a focal distance.

(B72) The multifocal lens of one or more of the above B examples,wherein the aberration profile includes higher order aberrations havingat least one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0).

(B73) The multifocal lens of one or more of the above B examples,wherein the aberration profile provides, for a model eye with no, orsubstantially no, aberrations and an on-axis length equal to the focaldistance: the retinal image quality (RIQ) with a through focus slopethat degrades in a direction of eye growth; and the RIQ of at least 0.3;wherein the RIQ is visual Strehl Ratio measured along the optical axisfor at least one pupil diameter in the range 3 mm to 6 mm, over aspatial frequency range of 0 to 30 cycles/degree inclusive and at awavelength selected from within the range 540 nm to 590 nm inclusive.

(B74) The multifocal lens of one or more of the above B examples,wherein the aberration profile provides, for a model eye with no, orsubstantially no, aberrations and an on-axis length equal to the focaldistance: the retinal image quality (RIQ) with a through focus slopethat improves in a direction of eye growth; and the RIQ of at least 0.3;wherein the RIQ is visual Strehl Ratio measured along the optical axisfor at least one pupil diameter in the range 3 mm to 6 mm, over aspatial frequency range of 0 to 30 cycles/degree inclusive and at awavelength selected from within the range 540 nm to 590 nm inclusive.

(B75) The multifocal lens of one or more of the above B examples,wherein the lens has an optical axis and an aberration profile about itsoptical axis, the aberration profile: having a focal distance; andincluding higher order aberrations having at least one of a primaryspherical aberration component C(4,0) and a secondary sphericalaberration component C(6,0), wherein the aberration profile provides,for a model eye with no, or substantially no, aberrations and an on-axislength equal, or substantially equal, to the focal distance: the RIQwith a through focus slope that degrades in a direction of eye growth;and the RIQ of at least 0.3; wherein the RIQ is visual Strehl Ratiomeasured along the optical axis for at least one pupil diameter in therange 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(B76) The multifocal lens of one or more of the above B examples,wherein the lens has an optical axis and an aberration profile about itsoptical axis, the aberration profile: having a focal distance; andincluding higher order aberrations having at least one of a primaryspherical aberration component C(4,0) and a secondary sphericalaberration component C(6,0), wherein the aberration profile provides,for a model eye with no, or substantially no, aberrations and an on-axislength equal, or substantially equal, to the focal distance: the RIQwith a through focus slope that improves in a direction of eye growth;and the RIQ of at least 0.3; wherein the RIQ is visual Strehl Ratiomeasured along the optical axis for at least one pupil diameter in therange 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(B77) The multifocal lens of one or more of the above B examples,wherein the focal distance is a prescription focal distance for amyopic, hyperopic, astigmatic, and/or presbyopic eye and wherein thefocal distance differs from the focal distance for a C(2,0) Zernikecoefficient of the aberration profile.

(B78) The multifocal lens of one or more of the above B examples,wherein the higher order aberrations include at least two sphericalaberration terms selected from the group C(4,0) to C(20,0).

(B79) The multifocal lens of one or more of the above B examples,wherein the higher order aberrations include at least three sphericalaberration terms selected from the group C(4,0) to C(20,0).

(B80) The multifocal lens of one or more of the above B examples,wherein the higher order aberrations include at least five sphericalaberration terms selected from the group C(4,0) to C(20,0).

(B81) The multifocal lens of one or more of the above B examples,wherein the average slope over a horizontal field of at least −20° to+20° degrades in a direction of eye growth.

(B82) The multifocal lens of one or more of the above B examples,wherein the average slope over a horizontal field of at least −20° to+20° improves in a direction of eye growth.

(B83) The multifocal lens of one or more of the above B examples,wherein the average slope over a vertical field of at least −20° to +20°degrades in a direction of eye growth.

(B84) The multifocal lens of one or more of the above B examples,wherein the average slope over a vertical field of at least −20° to +20°improves in a direction of eye growth.

(B85) The multifocal lens of one or more of the above B examples,wherein the slope for a substantial portion of the field angles over ahorizontal field of at least −20° to +20° degrades in a direction of eyegrowth.

(B86) The multifocal lens of one or more of the above B examples,wherein the substantial portion of the field angles over a horizontalfield is at least 75%, 85%, 95% or 99% of the field angles.

(B87) The multifocal lens of one or more of the above B examples,wherein the substantial portion of the field angles over a horizontalfield is every field angle.

(B88) The multifocal lens of one or more of the above B examples,wherein the slope for a substantial portion of the field angles over avertical field of at least −20° to +20° degrades in the direction of eyegrowth.

(B89) The multifocal lens of one or more of the above B examples,wherein the substantial portion of the field angles over a verticalfield is every angle.

(B90) The multifocal lens of one or more of the above B examples,wherein the slope for a substantial portion of the field angles over avertical field of at least −20° to +20° degrades in a direction of eyegrowth.

(B91) The multifocal lens of one or more of the above B examples,wherein the substantial portion of the field angles over a verticalfield is every angle.

(B92) The multifocal lens of one or more of the above B examples,wherein the substantial portion of the field angles over a verticalfield is at least 75%, 85%, 95% or 99% of the field angles.

(B93) The multifocal lens of one or more of the above B examples,wherein the aberration profile provides the RIQ of at least 0.3 at thefocal length for a substantial portion of pupil diameters in the range 3mm to 6 mm.

(B94) The multifocal lens of one or more of the above B examples,wherein the aberration profile provides the RIQ of at least 0.3 at thefocal length for a substantial portion of pupil diameters in the range 4mm to 5 mm.

(B95) The multifocal lens of one or more of the above B examples,wherein the aberration profile provides the RIQ with a through focusslope that degrades in a direction of eye growth when primary orsecondary astigmatism is added to the aberration profile.

(B96) The multifocal lens of one or more of the above B examples,wherein the aberration profile provides the RIQ with a through focusslope that improves in a direction of eye growth when primary orsecondary astigmatism is added to the aberration profile.

(B97) The multifocal lens of one or more of the above B examples,wherein the primary or secondary astigmatism is added to the desiredaberration profile by altering one or more of the following terms:C(2,−2), C(2,2), C(4,−2), C(4,2), C(6,−2) and/or C(6,2).

(B98) The multifocal lens of one or more of the above B examples,wherein the aberration profile provides the RIQ with a through focusslope that degrades in a direction of eye growth when secondaryastigmatism is added to the aberration profile.

(B99) The multifocal lens of one or more of the above B examples,wherein the secondary astigmatism is added to the desired aberrationprofile by altering one or more of the following terms: C(2,−2), C(2,2),C(4,−2), C(4,2), C(6,−2) and/or C(6,2).

(B100) The multifocal lens of one or more of the above B examples,wherein the RIQ is characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity function,CSF(F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1),where f specifies the tested spatial frequency, in the range of F_(min)to F_(max);FT denotes a 2D Fourier transform, for example a 2D fast Fouriertransform;A(ρ,θ) denotes the pupil amplitude function across the pupil diameter;W(ρ,θ) denotes wavefront of the test case measured for i=1 to 20

W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ);

Wdiff(ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(B101) The multifocal lens of one or more of the above B examples,wherein the RIQ is characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity function,CSF (F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1),where f specifies the tested spatial frequency, in the range of F_(min)to F_(max);FT denotes a 2D Fourier transform, for example a 2D fast Fouriertransform;A(ρ,θ) denotes the pupil amplitude function across the pupil diameter;W(ρ,θ) denotes wavefront of the test case measured for i=1 to k;where k is a positive integer;

W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ);

Wdiff(ρ, θ) denotes wavefront of the diffraction limited case;

ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; and

λ denotes wavelength.

(B102) The multifocal lens of one or more of the above B examples,wherein the multifocal lens includes an optical axis and an aberrationprofile along the optical axis that provides: a focal distance for aC(2,0) Zernike coefficient term; a peak visual Strehl Ratio (‘firstvisual Strehl Ratio’) within a through focus range, and a visual StrehlRatio that remains at or above a second visual Strehl Ratio over thethrough focus range that includes said focal distance, wherein thevisual Strehl Ratio is measured for a model eye with no, orsubstantially no, aberration and is measured along the optical axis forat least one pupil diameter in the range 3 mm to 5 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive, at a wavelengthselected from within the range 540 nm to 590 nm inclusive, and whereinthe first visual Strehl Ratio is at least 0.35, the second visual StrehlRatio is at least 0.1 and the through focus range is at least 1.8Dioptres.

(B103) The multifocal lens of one or more of the above B examples,wherein the multifocal lens includes an optical axis and an aberrationprofile along the optical axis that provides: a focal distance for aC(2,0) Zernike coefficient term; a peak visual Strehl Ratio (‘firstvisual Strehl Ratio’) within a through focus range, and a visual StrehlRatio that remains at or above a second visual Strehl Ratio over thethrough focus range that includes said focal distance, wherein thevisual Strehl Ratio is measured for a model eye with no aberration andis measured along the optical axis for at least one pupil diameter inthe range 3 mm to 5 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive, at a wavelength selected from within the range540 nm to 590 nm inclusive, and wherein the first visual Strehl Ratio isat least 0.35, the second visual Strehl Ratio is at least 0.1 and thethrough focus range is at least 1.8 Dioptres.

(B104) The multifocal lens of one or more of the above B examples,wherein the first visual Strehl Ratio is at least 0.3, 0.35, 0.4, 0.5,0.6, 0.7 or 0.8.

(B105) The multifocal lens of one or more of the above B examples,wherein the second visual Strehl Ratio is at least 0.1, 0.12, 0.15, 0.18or 0.2.

(B106) The multifocal lens of one or more of the above B examples,wherein the through focus range is at least 1.7, 1.8, 1.9, 2, 2.1, 2.25or 2.5 Dioptres.

(B107) The multifocal lens of one or more of the above B examples,wherein the lens has a prescription focal distance located within 0.75,0.5, 0.3, or 0.25 Dioptres, inclusive, of an end of the through focusrange.

(B108) The multifocal lens of one or more of the above B examples,wherein the end of the through focus range is the negative power end.

(B109) The multifocal lens of one or more of the above B examples,wherein the end of the through focus range is the positive power end.

(B110) The multifocal lens of one or more of the above B examples,wherein the visual Strehl Ratio remains at or above the second visualStrehl Ratio over the through focus range and over a range of pupildiameters of at least 1 mm, 1.5 mm, 2 mm, 2.5 mm, or 3 mm.

(B111) The multifocal lens of one or more of the above B examples,wherein the combination of higher order aberrations includes at leastone of primary spherical aberration and secondary spherical aberration.

(B112) The multifocal lens of one or more of the above B examples,wherein the higher order aberrations include at least two, three, orfive spherical aberration terms selected from the group C(4,0) toC(20,0).

(B113) The multifocal lens of one or more of the above B examples,wherein the aberration profile is substantially charactered using onlyspherical aberration Zernike coefficients C(4,0) to C(20,0).

(B114) The multifocal lens of one or more of the above B examples,wherein the RIQ for a substantial portion of the angles over ahorizontal field of at least −10° to +10°, −20° to +20° or −30° to +30°is at least 0.4.

(B115) The multifocal lens of one or more of the above B examples,wherein the RIQ for a substantial portion of the angles over ahorizontal field of at least −10° to +10°, −20° to +20° or −30° to +30°is at least 0.35.

(B116) The multifocal lens of one or more of the above B examples,wherein the RIQ for a substantial portion of the angles over ahorizontal field of at least −10° to +10°, −20° to +20° or −30° to +30°is at least 0.3.

(B117) The multifocal lens of one or more of the above B examples,wherein the lens is one or more of the following: contact lens, cornealonlays, corneal inlays, anterior chamber intraocular lens or posteriorchamber intraocular lens.

(B118) The multifocal lens of one or more of the above B examples,wherein the lens is one of the following: contact lens, corneal onlays,corneal inlays, anterior chamber intraocular lens or posterior chamberintraocular lens.

(B119) The multifocal lens of one or more of the above B examples,wherein a first multifocal lens is provided based on one or more of theabove of the B examples and a second multifocal lens is provided basedon one or more of the B examples to form a pair of lenses.

(B120) The multifocal lens of one or more of the above B examples,wherein the first multifocal lens is provided based on one or more ofthe B examples and a second lens is provided to form a pair of lenses.

(B121) The multifocal lens of one or more of the above B examples,wherein a pair of multifocal lenses are provided for use by anindividual to substantially correct the individual's vision.

(B122) The multifocal lens of one or more of the above B examples,wherein the aberration profile is an aberration pattern.

(B123) A method for making or using one or more of the multifocal lensesof one or more of the above B examples.

Example Set C

(C1) A lens comprising: an optical axis; at least two optical surfaces;wherein the lens is configured to provide a visual performance on apresbyopic eye substantially equivalent to the visual performance of asingle-vision lens on the pre-presbyopic eye; and wherein the lens hasan aperture size greater than 1.5 mm.

(C2) A lens comprising: an optical axis; at least two optical surfaces;wherein the lens is configured to provide a visual performance on apresbyopic eye substantially equivalent to the visual performance of acorrectly prescribed single-vision lens on the pre-presbyopic eye; andwherein the lens has an aperture size greater than 1.5 mm.

(C3) A lens comprising: an optical axis; at least two optical surfaces;wherein the lens is configured to provide a visual performance for apresbyopic condition substantially equivalent to the visual performanceof an appropriately prescribed single-vision lens for the pre-presbyopiccondition; and wherein the lens has an aperture size greater than 1.5mm.

(C4) A lens comprising: an optical axis; at least two optical surfaces;wherein the lens is configured to provide a visual performance on apresbyopic eye substantially equivalent to the visual performance of aeffectively prescribed single-vision lens on the pre-presbyopic eye; andwherein the lens has an aperture size greater than 1.5 mm.

(C5) The lens of one or more of the above of the C examples, wherein thelens is configured based on an aberration profile associated with theoptical axis; the aberration profile is comprised of a defocus term andat least two spherical aberration terms; and the lens is configured toprovide the visual performance, along a range of substantiallycontinuous visual distances, including near, intermediate and fardistances.

(C6) The lens of one or more of the above C examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(C7) The lens of one or more of the above C examples, wherein the amountof light passing through the lens is at least 80%, 85%, 90%, 95% or 99%.

(C8) The lens of one or more of the above of the C examples, wherein thelens is configured to provide the visual performance, alongsubstantially continuous visual distances, including substantially neardistances, substantially intermediate distances, and substantially fardistances.

(C9) The lens of one or more of the above of the C examples, wherein thelens is configured to provide the visual performance, along continuousvisual distances, including near distances, intermediate distances, andfar distances.

(C10) The lens of one or more of the above of the C examples, whereinthe lens is configured to provide the visual performance, along a rangeof visual distances, including near, intermediate and far distances.

(C11) The lens of one or more of the above of the C examples, whereinthe aberration profile is comprised of the defocus term, the at leasttwo spherical aberration terms and at least one asymmetric higher orderaberration term.

(C12) The lens of one or more of the above of the C examples, whereinthe lens is characterised in part by the aberration profile associatedwith the optical axis of the lens.

(C13) The lens of one or more of the above C examples, wherein thesingle-vision lens is one of the following: prescribed, correctlyprescribed, appropriately prescribed, properly prescribed or effectivelyprescribed.

(C14) The lens of one or more of the above C examples, wherein the lensis one or more of the following: contact lens, corneal onlays, cornealinlays, intra-ocular contact lens, intraocular lens, anterior chamberintraocular lens and posterior chamber intraocular lens.

(C15) The lens of one or more of the above C examples, wherein the lensis one of the following: contact lens, corneal onlays, corneal inlays,intra-ocular contact lens, intraocular lens, anterior chamberintraocular lens or posterior chamber intraocular lens.

(C16) The lens of one or more of the above C examples, wherein thesingle-vision lens is a lens with a substantially constant power acrossa substantial portion of an optic zone of the single-vision lens.

(C17) The lens of one or more of the above C examples, wherein thesingle-vision lens is a lens with a constant power across a portion ofan optic zone of the single-vision lens.

(C18) The lens of one or more of the above C examples, wherein thesingle-vision lens is a lens with a substantially constant power acrossone or more portions of the optic zone of the single-vision lens.

(C19) The lens of one or more of the above C examples, wherein thesingle-vision lens is a lens with a constant power across one or moreportions of the optic zone of the single-vision lens.

(C20) The lens of one or more of the above C examples, wherein the lensis configured to optically correct or mitigate presbyopia.

(C21) The lens of one or more of the above C examples, wherein the lensis configured to alter, or substantially alter, a presbyopic conditionto a non-presbyopic condition.

(C22) The lens of one or more of the above C examples, wherein the lensis used for at least correcting a presbyopic eye condition and when usedprovides a best available fit to adjust the vision of the user towardssubstantial normal vision.

(C23) The lens of one or more of the above C examples, wherein the lensis further characterised by minimal, or no, ghosting at near,intermediate and far distances.

(C24) The lens of one or more of the above C examples, wherein the lensis further configured to provide minimal, or no, ghosting at near,intermediate and far distances.

(C25) The lens of one or more of the above C examples, wherein the lensis further configured to provide a sufficient lack of ghosting in asubstantial portion of near, intermediate and far distances.

(C26) The lens of one or more of the above C examples, wherein the lensis further configured to provide a sufficient lack of ghosting in asubstantial portion of two or more of the following: near, intermediateand far distances.

(C27) The lens of one or more of the above C examples, wherein the lensis further configured to provide a sufficient lack of ghosting in two ormore of the following: near, intermediate and far distances.

(C28) The lens of one or more of the above C examples, wherein the lensis further configured to provide the RIQ of at least 0.1, 0.12, 0.14,0.16, 0.18 or 0.2 in the near distance range, the RIQ of at least 0.3,0.32, 0.34, 0.36, 0.38 or 0.4 in the intermediate distance range and theRIQ of at least 0.4, 0.45, 0.5, 0.6 or 0.7 in the far distance range.

(C29) The lens of one or more of the above C examples, wherein the lensis further configured to provide the RIQ of at least 0.15 in the neardistance range, the RIQ of at least 0.25 in the intermediate distancerange and the RIQ of at least 0.3 in the far distance range.

(C30) The lens of one or more of the above C examples, wherein the lensis further configured to provide the RIQ of at least 0.2 in the neardistance range, the RIQ of at least 0.3 in the intermediate distancerange and the RIQ of at least 0.4 in the far distance range.

(C31) The lens of one or more of the above C examples, wherein the lensis further configured to provide two or more of the following: the RIQof at least 0.1, 0.12, 0.14, 0.16, 0.18 or 0.2 in the near distancerange, the RIQ of at least 0.3, 0.32, 0.34, 0.36, 0.38 or 0.4 in theintermediate distance range and the RIQ of at least 0.4, 0.45, 0.5, 0.6or 0.7 in the far distance range.

(C32) The lens of one or more of the above C examples, wherein RIQs areselected in the near, intermediate and far distance ranges such that thelens is configured to provide minimal, or no, ghosting in near,intermediate and far distances.

(C33) The lens of one or more of the above C examples, wherein the lensis configured to substantially eliminate, or substantially reduce,ghosting at near, intermediate and far distances.

(C34) The lens of one or more of the above C examples, wherein neardistance is the range of 33 cm to 50 cm or 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm, 50 cm to 80 cm or 50 cm to 70cm; and far distance is the range of 100 cm or greater, 80 cm or greateror 70 cm or greater.

(C35) The lens of one or more of the above C examples, wherein neardistance is the range of 33 cm to 50 cm or 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm, 50 cm to 80 cm or 50 cm to 70cm; and far distance is the range of 100 cm or greater, 80 cm or greateror 70 cm or greater and the near, intermediate and far distances aredetermined by the distance from the object being focused on.

(C36) The lens of one or more of the above C examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm orgreater.

(C37) The lens of one or more of the above C examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm orgreater and the near, intermediate and far distances are determined bythe distance from the object being focused on.

(C38) The lens of one or more of the above C examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm tooptical infinity.

(C39) The lens of one or more of the above C examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm tooptical infinity and the near, intermediate and far distances aredetermined by the distance from the object being focused on.

(C40) The lens of one or more of the above C examples, wherein the lensis configured to minimize, or reduce, ghosting at near, intermediate andfar distances when used on the pre-presbyopic eye.

(C41) The lens of one or more of the above C examples, wherein ghostingis measured when the lens is used on the pre-presbyopic eye.

(C42) The lens of one or more of the above C examples, wherein the rangeof substantially continuous distances is continuous.

(C43) The lens of one or more of the above C examples, wherein the rangeof substantially continuous distances is continuous and goes from 40 cmto optical infinity.

(C44) The lens of one or more of the above C examples, wherein the rangeof substantially continuous distances is from 33 cm to optical infinity.

(C45) The lens of one or more of the above C examples, wherein the lensis configured such that at least 40%, 50%, 60% or 70% of a randomlyselected group of 15 affected individuals in the near, intermediate andfar distance ranges perceive minimal, or no, ghosting at near,intermediate and far distances.

(C46) The lens of one or more of the above C examples, wherein the lensis configured such that at least 60%, 70%, 80% or 90% of a randomlyselected group of 15 affected individuals in the near, intermediate andfar distance ranges perceive minimal, or no, ghosting at near,intermediate and far distances.

(C47) The lens of one or more of the above C examples, wherein thesingle vision lens provides a visual acuity for the user of one or moreof the following: at least 20/20, at least 20/30, at least 20/40, atleast about 20/20, at least about 20/30 and at least about 20/40, at farvisual distance.

(C48) The lens of one or more of the above C examples, wherein theaberration profile is comprised of the defocus term and the at leasttwo, two or more, three, three or more, four, four or more, five, fiveor more, six, six or more, seven, seven or more, eight, eight or more,ten, or ten or more spherical aberration terms.

(C49) The lens of one or more of the above C examples, wherein theaberration profile is comprised of the defocus term and the at leasttwo, three, four, five, six, seven, eight, or at least ten sphericalaberration terms.

(C50) The multifocal lens of one or more of the above C examples,wherein the aberration profile is comprised of a defocus term andspherical aberration terms between C(4,0) and C(6,0), C(4,0) and C(8,0),C(4,0) and C(10,0), C(4,0) and C(12,0), C(4,0) and C(14,0), C(4,0) andC(16,0), C(4,0) and C(18,0) or C(4,0) and C(20,0).

(C51) The lens of one or more of the above C examples, wherein thebest-corrected visual acuity is a visual acuity that cannot besubstantially improved by further manipulating the power of the singlevision lens.

(C52) The lens of one or more of the above C examples, wherein the leastone aberration profile is along the optical axis of the lens.

(C53) The lens of one or more of the above C examples, wherein theaberration profile includes higher order aberrations having at least oneof a primary spherical aberration component C(4,0) and a secondaryspherical aberration component C(6,0).

(C54) The lens of one or more of the above C examples, wherein theaberration profile provides, for a model eye with no aberrations and anon-axis length equal to the focal distance: the RIQ with a through focusslope that degrades in a direction of eye growth; and the RIQ of atleast 0.30; wherein the RIQ is visual Strehl Ratio measured along theoptical axis for at least one pupil diameter in the range 3 mm to 6 mm,over a spatial frequency range of 0 to 30 cycles/degree inclusive and ata wavelength selected from within the range 540 nm to 590 nm inclusive.

(C55) The lens of one or more of the above C examples, wherein theaberration profile provides, for a model eye with no aberrations and anon-axis length equal to the focal distance: the RIQ with a through focusslope that improves in a direction of eye growth; and the RIQ of atleast 0.3; wherein the RIQ is visual Strehl Ratio measured along theoptical axis for at least one pupil diameter in the range 3 mm to 6 mm,over a spatial frequency range of 0 to 30 cycles/degree inclusive and ata wavelength selected from within the range 540 nm to 590 nm inclusive.

(C56) The lens of one or more of the above C examples, wherein the lenshas the optical axis and the aberration profile about the lens opticalaxis, the aberration profile: having the focal distance; and includinghigher order aberrations having the at least one of a primary sphericalaberration component C(4,0) and the secondary spherical aberrationcomponent C(6,0), wherein the aberration profile provides, for the modeleye with no aberrations and an on-axis length equal to the focaldistance: the RIQ with a through focus slope that degrades in adirection of eye growth; and the RIQ of at least 0.3; wherein the RIQ isvisual Strehl Ratio measured along the optical axis for the at least onepupil diameter in the range 3 mm to 6 mm, over a spatial frequency rangeof 0 to 30 cycles/degree inclusive and at a wavelength selected fromwithin the range 540 nm to 590 nm inclusive.

(C57) The lens of one or more of the above C examples, wherein the focaldistance is a prescription focal distance for a myopic eye and whereinthe focal distance differs from the focal distance for a C(2,0) Zernikecoefficient of the aberration profile.

(C58) The lens of one or more of the above C examples, wherein thehigher order aberrations include at least two spherical aberration termsselected from the group C(4,0) to C(20,0).

(C59) The lens of one or more of the above C examples, wherein thehigher order aberrations include at least three spherical aberrationterms selected from the group C(4,0) to C(20,0).

(C60) The lens of one or more of the above C examples, wherein thehigher order aberrations include at least five spherical aberrationterms selected from the group C(4,0) to C(20,0).

(C61) The lens of one or more of the above C examples, wherein theaverage slope over a horizontal field of at least −20° to +20° degradesin a direction of eye growth.

(C62) The lens of one or more of the above C examples, wherein theaverage slope over a vertical field of at least −20° to +20° degrades ina direction of eye growth.

(C63) The lens of one or more of the above C examples, wherein the slopefor a substantial portion of the field angles over a horizontal field ofat least −20° to +20° degrades in a direction of eye growth.

(C64) The lens of one or more of the above C examples, wherein the slopefor a substantial portion of the field angles over a vertical field ofat least −20° to +20° degrades in the direction of eye growth.

(C65) The lens of one or more of the above C examples, wherein thesubstantial portion of the field angles over the vertical field is everyangle.

(C66) The lens of one or more of the above C examples, wherein thesubstantial portion of the field angles over a horizontal field is everyfield angle.

(C67) The lens of one or more of the above C examples, wherein the slopefor a substantial portion of the field angles over a vertical field ofat least −20° to +20° degrades in a direction of eye growth.

(C68) The lens of one or more of the above C examples, wherein thesubstantial portion of the field angles over a vertical field is everyangle.

(C69) The lens of one or more of the above C examples, wherein theaberration profile provides the RIQ of at least 0.3 at the focal lengthfor a substantial portion of pupil diameters in the range 3 mm to 6 mm.

(C70) The lens of one or more of the above C examples, wherein theaberration profile provides the RIQ of at least 0.3 at the focal lengthfor a substantial portion of pupil diameters in the range 4 mm to 5 mm.

(C71) The lens of one or more of the above C examples, wherein theaberration profile provides the RIQ with a through focus slope thatdegrades in a direction of eye growth when primary astigmatism is addedto the aberration profile.

(C72) The lens of one or more of the above C examples, wherein theaberration profile provides the RIQ with a through focus slope thatdegrades in a direction of eye growth when secondary astigmatism isadded to the aberration profile.

(C73) The lens of one or more of the above C examples, wherein the RIQis characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity function,CSF(F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1)where f specifies the tested spatial frequency, in the range of F_(min)to F_(max);FT denotes a 2D fast Fourier transform;A(ρ,θ) denotes the pupil amplitude function across the pupil diameter;W(ρ,θ) denotes wavefront of the test case measured for i=1 to 20

W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ);

Wdiff(ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(C74) The lens of one or more of the above C examples, wherein the RIQis characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity function,CSF (F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1)where f specifies the tested spatial frequency, in the range of F_(min)to F_(max);FT denotes a 2D Fourier transform, for example a 2D fast Fouriertransform;A (ρ, θ) denotes the pupil amplitude function across the pupil diameter;W (ρ, θ) denotes wavefront of the test case measured for i=1 to k;wherein k is a positive integer;

W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ);

Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(C75) The lens of one or more of the above C examples, wherein the lensincludes the optical axis and the aberration profile about the opticalaxis that provides: the focal distance for the C(2,0) Zernikecoefficient term; a peak visual Strehl Ratio (‘first visual StrehlRatio’) within a through focus range, and a visual Strehl Ratio thatremains at or above a second visual Strehl Ratio over the through focusrange that includes the focal distance, wherein the visual Strehl Ratiois measured for the model eye with no aberration and is measured alongthe optical axis for at least one pupil diameter in the range 3 mm to 5mm, over the spatial frequency range of 0 to 30 cycles/degree inclusive,at the wavelength selected from within the range 540 nm to 590 nminclusive, and wherein the first visual Strehl Ratio is at least 0.35,the second visual Strehl Ratio is at least 0.1 and the through focusrange is at least 1.8 Dioptres.

(C76) The lens of one or more of the above C examples, wherein the firstvisual Strehl Ratio is at least 0.4, 0.5, 0.6, 0.7 or 0.8.

(C77) The lens of one or more of the above C examples, wherein thesecond visual Strehl Ratio is at least 0.1, 0.12, 0.14, 0.16, 0.18 or0.2.

(C78) The lens of one or more of the above C examples, wherein thethrough focus range is at least 1.7, 1.8, 1.9, 2, 2.1, 2.25 or 2.5Dioptres.

(C79) The lens of one or more of the above C examples, wherein the lenshas a prescription focal distance located within 0.75, 0.5, 0.3, or 0.25Dioptres, inclusive, of an end of the through focus range.

(C80) The lens of one or more of the above C examples, wherein the endof the through focus range is the negative power end.

(C81) The lens of one or more of the above C examples, wherein the endof the through focus range is the positive power end.

(C82) The lens of one or more of the above C examples, wherein thevisual Strehl Ratio remains at or above the second visual Strehl Ratioover the through focus range and over a range of pupil diameters of atleast 1 mm, 1.5 mm or 2 mm.

(C83) The lens of one or more of the above C examples, wherein thecombination of higher order aberrations includes at least one of primaryspherical aberration and secondary spherical aberration.

(C84) The lens of one or more of the above C examples, wherein thehigher order aberrations include at least two, three, or five sphericalaberration terms selected from the group C(4,0) to C(20,0).

(C85) The lens of one or more of the above C examples, wherein theaberration profile is substantially charactered using only sphericalaberration Zernike coefficients C (4, 0) to C (20, 0).

(C86) The lens of one or more of the above C examples, wherein the RIQfor a substantial portion of the angles over a horizontal field of atleast −10° to +10°, −20° to +20° or −30° to +30° is at least 0.3, 0.35or 0.4.

(C87) The lens of one or more of the above C examples, wherein the RIQfor every angle over a horizontal field of at least −10° to +10°, −20°to +20° or −30° to +30° is at least 0.3, 0.35 or 0.4.

(C88) The lens of one or more of the above C examples, wherein a firstlens is provided based on one or more of the C examples and a secondlens is provided based on one or more of the C examples to form a pairof lenses.

(C89) The lens of one or more of the above C examples, wherein a firstlens is provided based on one or more of the C examples and a secondlens is provided to form a pair of lenses.

(C90) The lens of one or more of the above C examples, wherein the pairof lenses are provide for use by an individual to substantially correctthe individuals version.

Example Set D

(D1) A lens for an eye, the lens having at least one optical axis and atleast one optical profile substantially about at least one optical axis,the optical profile comprising: at least one focal distance; and one ormore higher order aberrations, wherein the optical profile provides for:a model eye with substantially no aberrations and an on-axis lengthequal to, or substantially equal to, the desired focal distance; aretinal image quality (RIQ) with a through focus slope that degrades ina direction of eye growth; and a RIQ of at least 0.3; and wherein theRIQ is measured along the optical axis for at least one pupil diameterin the range 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(D2) A lens for an eye, the lens having at least one optical axis and atleast one optical profile substantially about at least one optical axis,the optical profile comprising: at least one focal distance; and one ormore higher order aberrations, wherein the optical profile provides for:a model eye with no aberrations and an on-axis length equal to thedesired focal distance; a retinal image quality (RIQ) with a throughfocus slope that degrades in a direction of eye growth; and a RIQ of atleast 0.3; and wherein the RIQ is measured along the optical axis for atleast one pupil diameter in the range 3 mm to 6 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive and at a wavelengthselected from within the range 540 nm to 590 nm inclusive.

(D3) A lens for an eye, the lens having an optical axis and at least oneoptical profile substantially about the optical axis the optical profilecomprising: at least one focal distance; and one or more higher orderaberrations, wherein the optical profile provides for a model eye withsubstantially no aberrations and an on-axis length equal to, orsubstantially equal to, the desired focal distance; a retinal imagequality (RIQ) with a through focus slope that improves in a direction ofeye growth; and a RIQ of at least 0.3; and wherein the RIQ is measuredalong the optical axis for at least one pupil diameter in the range 3 mmto 6 mm, over a spatial frequency range of 0 to 30 cycles/degreeinclusive and at a wavelength selected from within the range 540 nm to590 nm inclusive.

(D4) A lens for an eye, the lens having an optical axis and anaberration profile about the optical axis the aberration profilecomprising: a focal distance; and higher order aberrations having atleast one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0), wherein the aberrationprofile provides for: a model eye with no aberrations, or substantiallyno aberrations, and an on-axis length equal to the focal distance: aretinal image quality (RIQ) with a through focus slope that degrades ina direction of eye growth; and a RIQ of at least 0.3; wherein the RIQ isvisual Strehl Ratio measured substantially along the optical axis for atleast one pupil diameter in the range 3 mm to 6 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive and at a wavelengthselected from within the range 540 nm to 590 nm inclusive.

(D5) A lens for an eye, the lens having an optical axis and anaberration profile about the optical axis the aberration profilecomprising: a focal distance; and higher order aberrations having atleast one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0), wherein the aberrationprofile provides for: a model eye with no aberrations and an on-axislength equal to the focal distance; a retinal image quality (RIQ) with athrough focus slope that degrades in a direction of eye growth; and aRIQ of at least 0.3; wherein the RIQ is visual Strehl Ratio measuredsubstantially along the optical axis for at least one pupil diameter inthe range 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(D6) A lens for an eye, the lens having an optical axis and at least oneoptical profile substantially about the optical axis the optical profilecomprising: at least one focal distance; and one or more higher orderaberrations, wherein the optical profile provides for: a model eye withsubstantially no aberrations an on-axis length equal to, orsubstantially equal to, the desired focal distance; a retinal imagequality (RIQ) with a through focus slope that improves in a direction ofeye growth; and a RIQ of at least 0.3; and wherein the RIQ is visualStrehl Ratio measured substantially along the optical axis for at leastone pupil diameter in the range 3 mm to 6 mm, over a spatial frequencyrange of 0 to 30 cycles/degree inclusive and at a wavelength selectedfrom within the range 540 nm to 590 nm inclusive.

(D7) A lens for an eye, the lens having an optical axis and anaberration profile about the optical axis the aberration profilecomprising: a focal distance; and higher order aberrations having atleast one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0), wherein the aberrationprofile provides for: a model eye with no aberrations, or substantiallyno aberrations, and an on-axis length equal to the focal distance: aretinal image quality (RIQ) with a through focus slope that improves ina direction of eye growth; and a RIQ of at least 0.3; wherein the RIQ isvisual Strehl Ratio measured substantially along the optical axis for atleast one pupil diameter in the range 3 mm to 6 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive and at a wavelengthselected from within the range 540 nm to 590 nm inclusive.

(D8) A lens for an eye, the lens having an optical axis and a surfacestructure, wherein the surface structure is configured to generate anaberration profile about the optical axis, the aberration profilecomprising: a focal distance; and higher order aberrations having atleast one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0),wherein the aberrationprofile provides, for a model eye with no aberrations, or substantiallyno aberrations, and an on-axis length equal to the focal distance: aretinal image quality (RIQ) with a through focus slope that improves ina direction of eye growth; and a RIQ of at least 0.3; wherein the RIQ isvisual Strehl Ratio measured substantially along the optical axis for atleast one pupil diameter in the range 3 mm to 6 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive and at a wavelengthselected from within the range 540 nm to 590 nm inclusive.

(D9) A lens for an eye, the lens having an optical axis and at least oneoptical profile substantially about the optical axis, the opticalprofile comprising: at least one focal distance; and one or more higherorder aberrations, wherein the optical profile provides, for a model eyewith substantially no aberrations an on-axis length equal to, orsubstantially equal to, the desired focal distance; a retinal imagequality (RIQ) with a through focus slope that improves in a direction ofeye growth; and a RIQ of at least 0.3; wherein said RIQ is measuredsubstantially along the optical axis for at least one pupil.

(D10) The lens of one or more of the above D examples, wherein thesingle-vision lens is one or more of the following: prescribed,appropriately prescribed, correctly prescribed and effectivelyprescribed.

(D11) The lens of one or more of the above D examples, wherein thesingle-vision lens is a lens with a substantially constant power acrossa substantial portion of an optic zone of the single-vision lens.

(D12) The lens of one or more of the above D examples, wherein thesingle-vision lens is a lens with a constant power across a portion ofan optic zone of the single-vision lens.

(D13) The lens of one or more of the above D examples, wherein thesingle-vision lens is a lens with a substantially constant power acrossa portion of one or more optic zones of the single-vision lens.

(D14) The lens of one or more of the above of the above D examples,wherein the lens is used for a presbyopic eye.

(D15) The lens of one or more of the above D examples, wherein the lensis configured for a presbyopic eye.

(D16) The lens of one or more of the above D examples, wherein the lensis configured to optically correct or substantially correct presbyopia.

(D17) The lens of one or more of the above D examples, wherein the lensis configured to mitigate or substantially mitigate the opticalconsequences of presbyopia.

(D18) The lens of one or more of the above D examples, wherein the lensis configured to alter or substantially alter a presbyopic condition toa non-presbyopic condition.

(D19) The lens of one or more of the above D examples, wherein the lensis used for at least correcting a presbyopic eye condition and when usedprovides an appropriate correction to adjust the vision of the usertowards substantially normal non-presbyopic vision.

(D20) The lens of one or more of the above D examples, wherein normalvision is 6/6 or better.

(D21) The lens of one or more of the above D examples, wherein the lensis further characterised by minimal, substantially no or no, ghosting atnear, intermediate and far distances.

(D22) The lens of one or more of the above D examples, wherein the lensis further characterised by minimal, substantially no or no, ghosting atnear distances, intermediate distances and far distances.

(D23) The lens of one or more of the above D examples, wherein the lensis further configured to provide minimal, substantially no or no,ghosting at near, intermediate and far distances.

(D24) The lens of one or more of the above D examples, wherein theminimal ghosting is a lack of an undesired secondary image appearing atthe image plane of the optical system.

(D25) The lens of one or more of the above D examples, wherein theminimal ghosting is a lack of an undesired secondary image appearing onthe retina of the eye.

(D26) The lens of one or more of the above D examples, wherein theminimal ghosting is a lack of an undesired double image appearing on theretina of the eye.

(D27) The lens of one or more of the above D examples, wherein theminimal ghosting is a lack of false out-of-focus image appearing alongside of the primary image in an optical system.

(D28) The lens of one or more of the above D examples, wherein the lensis further configured to provide a sufficient lack of ghosting in aportion of near, intermediate and far distances.

(D29) The lens of one or more of the above D examples, wherein the lensis further configured to provide a sufficient lack of ghosting at neardistances, intermediate distances and far distances.

(D30) The lens of one or more of the above D examples, wherein the lensis further configured to provide a sufficient lack of ghosting in aportion of two or more of the following: near, intermediate and fardistances.

(D31) The lens of one or more of the above D examples, wherein lack ofghosting is lack of undesired image appearing at the image plane of theoptical system.

(D32) The lens of one or more of the above D examples, wherein lack ofghosting is a lack of false out of focus images appearing along side ofthe primary image in an optical system.

(D33) The lens of one or more of the above D examples, wherein the lensis further configured to provide a sufficient lack of ghosting in aportion of two or more of the following: near distances, intermediatedistances and far distances.

(D34) The lens of one or more of the above D examples, wherein the lensis further configured to provide the RIQ of at least 0.1, 0.13, 0.17,0.2, 0.225, or 0.25 in the near distance range, the RIQ of at least0.27, 0.3, 0.33, 0.35, 0.37 or 0.4 in the intermediate distance rangeand the RIQ of at least 0.35, 0.37, 0.4, 0.42, 0.45, 0.47, or 0.5 in thefar distance range.

(D35) The lens of one or more of the above D examples, wherein the lensis further configured to provide two or more of the following: the RIQof at least 0.1, 0.13, 0.17, 0.2, 0.225, or 0.25 in the near distancerange, the RIQ of at least 0.27, 0.3, 0.33, 0.35, 0.37 or 0.4 in theintermediate distance range and the RIQ of at least 0.35, 0.37, 0.4,0.42, 0.45, 0.47, or 0.5 in the far distance range.

(D36) The lens of one or more of the above D examples, wherein the RIQsare selected in the near, intermediate and far distance ranges such thatthe lens is configured to provide minimal, or no, ghosting in near,intermediate and far distances.

(D37) The lens of one or more of the above D examples, wherein the lensis configured to substantially eliminate, or substantially reduce,ghosting at near, intermediate and far distances.

(D38) The lens of one or more of the above D examples, wherein the lensis configured to substantially eliminate, or substantially reduce,ghosting at near distances, intermediate distances and far distances.

(D39) The lens of one or more of the above D examples, wherein neardistance is the range of 33 cm to 50 cm or 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm, 50 cm to 80 cm or 50 cm to 70cm; and far distance is the range of 100 cm or greater, 80 cm or greateror 70 cm or greater.

(D40) The lens of one or more of the above D examples, wherein neardistance is the range of 33 cm to 50 cm or 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm, 50 cm to 80 cm or 50 cm to 70cm; and far distance is the range of 100 cm or greater, 80 cm or greateror 70 cm or greater and the near, intermediate and far distances aredetermined by the distance from the object being focused on.

(D41) The lens of one or more of the above D examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm orgreater.

(D42) The lens of one or more of the above D examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm orgreater and the near, intermediate and far distances are determined bythe distance from the object being focused on.

(D43) The lens of one or more of the above D examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm tooptical infinity.

(D44) The lens of one or more of the above D examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm tooptical infinity and the near, intermediate and far distances aredetermined by the distance from the object being focused on.

(D45) The lens of one or more of the above D examples, wherein the lensis configured to minimize, or reduce, ghosting at near, intermediate andfar distances when used on an eye.

(D46) The lens of one or more of the above D examples, wherein the lensis configured to minimize, or reduce, ghosting at near distances,intermediate distances and far distances when used on an eye.

(D47) The lens of one or more of the above D examples, wherein the rangeof substantially continuous distances is continuous.

(D48) The lens of one or more of the above D examples, wherein the rangeof substantially continuous distances is continuous and goes from 40 cmto optical infinity.

(D49) The lens of one or more of the above D examples, wherein the rangeof substantially continuous distances is from 33 cm to optical infinity.

(D50) The lens of one or more of the above D examples, wherein the lensis configured such that at least 40%, 50%, 60% or 70% of a randomlyselected group of 15 affected individuals in the near distances,intermediate distances and far distances perceive minimal, or no,ghosting at near distances, intermediate distances and far distances.

(D51) The lens of one or more of the above D examples, wherein the lensis configured such that at least 60%, 70%, 80% or 90% of a randomlyselected group of 15 affected individuals in the intermediate distancesand far distances perceive minimal, or no, ghosting at intermediatedistances and far distances.

(D52) The lens of one or more of the above D examples, wherein thesingle vision lens provides a visual acuity for the user of one or moreof the following: at least 20/20, at least 20/30, at least 20/40, atleast about 20/20, at least about 20/30 and at least about 20/40, at farvisual distances.

(D53) The lens of one or more of the above D examples, wherein theaberration profile is comprised of a defocus term and at least two, twoor more, three, three or more, four, four or more, five, five or more,six, six or more, seven, seven or more, eight, eight or more, nine, nineor more, ten, or ten or more spherical aberration terms.

(D54) The lens of one or more of the above D examples, wherein theaberration profile is comprised of a defocus term and at least two,three, four, five, six, seven, eight, nine, or at least ten sphericalaberration terms.

(D55) The lens of one or more of the above D examples, wherein theaberration profile is comprised of a defocus term and sphericalaberration terms between C(4,0) and C(6,0), C(4,0) and C(8,0), C(4,0)and C(10,0), C(4,0) and C(12,0), C(4,0) and C(14,0), C(4,0) and C(16,0),C(4,0) and C(18,0), or C(4,0) and C(20,0).

(D56) The lens of one or more of the above D examples, wherein thesingle vision lens provides a visual acuity that is the best-correctedvisual acuity.

(D57) The lens of one or more of the above D examples, wherein thebest-corrected visual acuity is a visual acuity that cannot besubstantially improved by further manipulating the power of the singlevision lens.

(D58) The lens of one or more of the above D examples, wherein the lenshas two optical surfaces.

(D59) The lens of one or more of the above D examples, wherein the leastone aberration profile is along the optical axis of the lens.

(D60) The lens of one or more of the above D examples, wherein the lenshas a focal distance.

(D61) The lens of one or more of the above D examples, wherein theaberration profile includes higher order aberrations having at least oneof a primary spherical aberration component C(4,0) and a secondaryspherical aberration component C(6,0).

(D62) The lens of one or more of the above D examples, wherein the focaldistance is a prescription focal distance for a myopic, hyperopic,astigmatic, and/or presbyopic eye and wherein the focal distance differsfrom the focal distance for a C(2,0) Zernike coefficient of theaberration profile.

(D63) The lens of one or more of the above D examples, wherein thehigher order aberrations include at least two spherical aberration termsselected from the group C(4,0) to C(20,0).

(D64) The lens of one or more of the above D examples, wherein thehigher order aberrations include at least three spherical aberrationterms selected from the group C(4,0) to C(20,0).

(D65) The lens of one or more of the above D examples, wherein thehigher order aberrations include at least five spherical aberrationterms selected from the group C(4,0) to C(20,0).

(D66) The lens of one or more of the above D examples, wherein theaverage slope over a horizontal field of at least −20° to +20° degradesin a direction of eye growth.

(D67) The lens of one or more of the above D examples, wherein theminimal ghosting is a lack of an undesired secondary image appearing atthe image plane of the optical system.

(D68) The lens of one or more of the above D examples, wherein theminimal ghosting is a lack of an undesired secondary image appearing onthe retina of the eye.

(D69) The lens of one or more of the above D examples, wherein theminimal ghosting is a lack of an undesired double image appearing on theretina of the eye.

(D70) The lens of one or more of the above D examples, wherein theminimal ghosting is a lack of false out-of-focus image appearing alongside of the primary image in an optical system.

(D71) The lens of one or more of the above D examples, wherein theaverage slope over a horizontal field of at least −20° to +20° improvesin a direction of eye growth.

(D72) The lens of one or more of the above D examples, wherein theaverage slope over a vertical field of at least −20° to +20° degrades ina direction of eye growth.

(D73) The lens of one or more of the above D examples, wherein theaverage slope over a vertical field of at least −20° to +20° improves ina direction of eye growth.

(D74) The lens of one or more of the above D examples, wherein the slopefor a substantial portion of the field angles over a horizontal field ofat least −20° to +20° degrades in a direction of eye growth.

(D75) The lens of one or more of the above D examples, wherein thesubstantial portion of the field angles over a horizontal field is atleast 75%, 85%, 95% or 99% of the field angles.

(D76) The lens of one or more of the above D examples, wherein thesubstantial portion of the field angles over a horizontal field is everyfield angle.

(D77) The lens of one or more of the above D examples, wherein the slopefor a substantial portion of the field angles over a vertical field ofat least −20° to +20° degrades in a direction of eye growth.

(D78) The lens of one or more of the above D examples, wherein thesubstantial portion of the field angles over a vertical field is everyangle.

(D79) The lens of one or more of the above D examples, wherein thesubstantial portion of the field angles over a vertical field is atleast 75%, 85%, 95% or 99% of the field angles.

(D80) The lens of one or more of the above D examples, wherein theaberration profile provides the RIQ of at least 0.3 at the focal lengthfor a substantial portion of pupil diameters in the range 3 mm to 6 mm.

(D81) The lens of one or more of the above D examples, wherein theaberration profile provides the RIQ of at least 0.3 at the focal lengthfor a substantial portion of pupil diameters in the range 4 mm to 5 mm.

(D82) The lens of one or more of the above D examples, wherein theaberration profile provides the RIQ with a through focus slope thatdegrades in a direction of eye growth when primary or secondaryastigmatism is added to the aberration profile.

(D83) The lens of one or more of the above D examples, wherein theaberration profile provides the RIQ with a through focus slope thatimproves in a direction of eye growth when primary or secondaryastigmatism is added to the aberration profile.

(D84) The lens of one or more of the above D examples, wherein theprimary or secondary astigmatism is added to the desired aberrationprofile by altering one or more of the following terms: C(2,−2), C(2,2),C(4,−2), C(4,2), C(6,−2), and/or C(6,2).

(D85) The lens of one or more of the above D examples, wherein theaberration profile provides the RIQ with a through focus slope thatdegrades in a direction of eye growth when secondary astigmatism isadded to the aberration profile.

(D86) The lens of one or more of the above D examples, wherein thesecondary astigmatism is added to the desired aberration profile byaltering one or more of the following terms: C(2,−2), C(2,2), C(4,−2),C(4,2), C(6,−2), and/or C(6,2).

(D87) The lens of one or more of the above D examples, wherein the RIQis characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity function,CSF (F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1),where f specifies the tested spatial frequency, in the range of F_(min)to F_(max);FT denotes a 2D fast Fourier transform;A (ρ, θ) denotes the pupil amplitude function across the pupil diameter;W (ρ, θ) denotes wavefront of the test case measured for i=1 to 20

W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ);

Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(D88) The lens of one or more of the above D examples, wherein the RIQis characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity function,CSF (F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1),where f specifies the tested spatial frequency, in the range of F_(min)to F_(max);FT denotes a 2D Fourier transform, for example a 2D fast Fouriertransform;A (ρ, θ) denotes the pupil amplitude function across the pupil diameter;W (ρ, θ) denotes wavefront of the test case measured for i=1 to k;where k is a positive integer;

W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ);

Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(D89) The lens of one or more of the above D examples, wherein the lensincludes an optical axis and an aberration profile along the opticalaxis that provides: a focal distance for a C(2,0) Zernike coefficientterm; a peak visual Strehl Ratio (‘first visual Strehl Ratio’) within athrough focus range, and a visual Strehl Ratio that remains at or abovea second visual Strehl Ratio over the through focus range that includessaid focal distance, wherein the visual Strehl Ratio is measured for amodel eye with no, or substantially no, aberration and is measured alongthe optical axis for at least one pupil diameter in the range 3 mm to 5mm, over a spatial frequency range of 0 to 30 cycles/degree inclusive,at a wavelength selected from within the range 540 nm to 590 nminclusive, and wherein the first visual Strehl Ratio is at least 0.35,the second visual Strehl Ratio is at least 0.1 and the through focusrange is at least 1.8 Dioptres.

(D90) The lens of one or more of the above D examples, wherein the lensincludes an optical axis and an aberration profile along the opticalaxis that provides: a focal distance for a C(2,0) Zernike coefficientterm; a peak visual Strehl Ratio (‘first visual Strehl Ratio’) within athrough focus range, and a visual Strehl Ratio that remains at or abovea second visual Strehl Ratio over the through focus range that includessaid focal distance, wherein the visual Strehl Ratio is measured for amodel eye with no aberration and is measured along the optical axis forat least one pupil diameter in the range 3 mm to 5 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive, at a wavelengthselected from within the range 540 nm to 590 nm inclusive, and whereinthe first visual Strehl Ratio is at least 0.35, the second visual StrehlRatio is at least 0.1 and the through focus range is at least 1.8Dioptres.

(D91) The lens of one or more of the above D examples, wherein the firstvisual Strehl Ratio is at least 0.3, 0.35, 0.4, 0.5, 0.6, 0.7 or 0.8.

(D92) The lens of one or more of the above D examples, wherein thesecond visual Strehl Ratio is at least 0.1, 0.12, 0.15, 0.18 or 0.2.

(D93) The lens of one or more of the above D examples, wherein thethrough focus range is at least 1.7, 1.8, 1.9, 2, 2.1, 2.25 or 2.5Dioptres.

(D94) The lens of one or more of the above D examples, wherein the lenshas a prescription focal distance located within 0.75, 0.5, 0.3, or 0.25Dioptres, inclusive, of an end of the through focus range.

(D95) The lens of one or more of the above D examples, wherein the endof the through focus range is the negative power end.

(D96) The lens of one or more of the above D examples, wherein the endof the through focus range is the positive power end.

(D97) The lens of one or more of the above D examples, wherein thevisual Strehl Ratio remains at or above the second visual Strehl Ratioover the through focus range and over a range of pupil diameters of atleast 1 mm, 1.5 mm, 2 mm, 2.5 mm, or 3 mm.

(D98) The lens of one or more of the above D examples, wherein thecombination of higher order aberrations includes at least one of primaryspherical aberration and secondary spherical aberration.

(D99) The lens of one or more of the above D examples, wherein thehigher order aberrations include at least two, three, or five sphericalaberration terms selected from the group C(4,0) to C(20,0).

(D100) The lens of one or more of the above D examples, wherein theaberration profile is substantially charactered using only sphericalaberration Zernike coefficients C (4, 0) to C (20, 0).

(D101) The lens of one or more of the above D examples, wherein the RIQfor a substantial portion of the angles over a horizontal field of atleast −10° to +10°, −20° to +20° or −30° to +30° is at least 0.4.

(D102) The lens of one or more of the above D examples, wherein the RIQfor a substantial portion of the angles over a horizontal field of atleast −10° to +10°, −20° to +20° or −30° to +30° is at least 0.35.

(D103) The lens of one or more of the above D examples, wherein the RIQfor a substantial portion of the angles over a horizontal field of atleast −10° to +10°, −20° to +20° or −30° to +30° is at least 0.3.

(D104) The lens of one or more of the above D examples, wherein the lensis one or more of the following: contact lens, corneal onlays, cornealinlays, anterior chamber intraocular lens or posterior chamberintraocular lens.

(D105) The lens of one or more of the above D examples, wherein the lensis one of the following: contact lens, corneal onlays, corneal inlays,anterior chamber intraocular lens or posterior chamber intraocular lens.

(D106) The lens of one or more of the above D examples, wherein a firstlens is provided based on one or more of the D examples and a secondlens is provided based on one or more of the D examples to form a pairof lenses.

(D107) The lens of one or more of the above D examples, wherein thefirst lens is provided based on one or more of the D examples and asecond lens is provided to form a pair of lenses.

(D108) The lens of one or more of the above D examples, wherein a pairof lenses are provided for use by an individual to substantially correctthe individual's vision.

(D109) A method for making or using one or more of the lenses of one ormore of the above D examples.

(D110) The lens of one or more of the above D examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(D111) The lens of one or more of the above D examples, wherein theamount of light passing through the lens is at least 80%, 85%, 90%, 95%or 99%.

Example Set E

(E1) A lens for an eye, the lens comprising: an optical axis; anaberration profile about the optical axis and having a focal distance;and at least two optical surfaces; and wherein the lens's opticalproperties can be characterised upon testing by at least the followingproperties: two or more higher order aberrations having one or more ofthe following components: a primary spherical aberration C(4,0), asecondary spherical aberration C(6,0), a tertiary spherical aberrationC(8,0), a quaternary spherical aberration C(10,0), a pentanary sphericalaberration C(12,0), a hexanary spherical aberration C(14,0), a heptanaryspherical aberration C(16,0), an octanary spherical aberration C(18,0)and a nanonary spherical aberration C(20,0); the aberration profile whentested on a model eye with no, or substantially no, aberrations andhaving an on-axis length equal, or substantially equal, to the focaldistance, results in a retinal image quality (RIQ) with a through focusslope so that the RIQ decreases in a direction of eye growth, where theRIQ is determined by a visual Strehl Ratio that is measuredsubstantially along the optical axis; and the RIQ is measured for amodel eye with no, or substantially no, aberration and is measured alongthe optical axis for at least one pupil diameter in the range 3 mm to 5mm, over a spatial frequency range of 0 to 30 cycles/degree inclusive,at a wavelength selected from within the range 540 nm to 590 nminclusive.

(E2) A lens for an eye, the lens comprising: an optical axis; anaberration profile about the optical axis and having a focal distance;and at least two optical surfaces; and wherein the lens's opticalproperties can be characterised upon testing by at least the followingproperties: two or more higher order aberrations having one or more ofthe following components: a primary spherical aberration C(4,0), asecondary spherical aberration C(6,0), a tertiary spherical aberrationC(8,0), a quaternary spherical aberration C(10,0), a pentanary sphericalaberration C(12,0), a hexanary spherical aberration C(14,0), a heptanaryspherical aberration C(16,0), an octanary spherical aberration C(18,0)and a nanonary spherical aberration C(20,0); the aberration profile whentested on a model eye with no aberrations and having an on-axis lengthequal to the focal distance, results in a retinal image quality (RIQ)with a through focus slope so that the RIQ decreases in a direction ofeye growth, where the RIQ is determined by a visual Strehl Ratio that ismeasured along the optical axis; and the RIQ is measured for a model eyewith no aberrations and is measured along the optical axis for at leastone pupil diameter in the range 3 mm to 5 mm, over a spatial frequencyrange of 0 to 30 cycles/degree inclusive, at a wavelength selected fromwithin the range 540 nm to 590 nm inclusive.

(E3) A lens for an eye, the lens comprising: an optical axis; anaberration profile about the optical axis and having a focal distance;and at least two optical surfaces; and wherein the lens's opticalproperties can be characterised upon testing by at least the followingproperties: two or more higher order aberrations having one or more ofthe following components: a primary spherical aberration C(4,0), asecondary spherical aberration C(6,0), a tertiary spherical aberrationC(8,0), a quaternary spherical aberration C(10,0), a pentanary sphericalaberration C(12,0), a hexanary spherical aberration C(14,0), a heptanaryspherical aberration C(16,0), an octanary spherical aberration C(18,0)and a nanonary spherical aberration C(20,0); the aberration profile whentested on a model eye with no aberrations and having an on-axis lengthequal to the focal distance, results in a retinal image quality (RIQ)with a through focus slope so that the RIQ increases in a direction ofeye growth, where the RIQ is determined by a visual Strehl Ratio that ismeasured along the optical axis; and the RIQ is measured for a model eyewith no aberrations and is measured along the optical axis for at leastone pupil diameter in the range 3 mm to 5 mm, over a spatial frequencyrange of 0 to 30 cycles/degree inclusive, at a wavelength selected fromwithin the range 540 nm to 590 nm inclusive.

(E4) A lens for an eye, the lens comprising: an optical axis; anaberration profile about the optical axis and having a focal distance;and at least two optical surfaces; and wherein the lens's opticalproperties can be characterised upon testing by at least the followingproperties: two or more higher order aberrations having one or more ofthe following components: a primary spherical aberration C(4,0), asecondary spherical aberration C(6,0), a tertiary spherical aberrationC(8,0), a quaternary spherical aberration C(10,0), a pentanary sphericalaberration C(12,0), a hexanary spherical aberration C(14,0), a heptanaryspherical aberration C(16,0), an octanary spherical aberration C(18,0)and a nanonary spherical aberration C(20,0); the aberration profile whentested on a model eye with no, or substantially no, aberrations andhaving an on-axis length equal, or substantially equal, to the focaldistance, results in a retinal image quality (RIQ) with a through focusslope so that the RIQ increases in a direction of eye growth, where theRIQ is determined by a visual Strehl Ratio that is measuredsubstantially along the optical axis; and the RIQ is measured for amodel eye with no, or substantially no, aberration and is measured alongthe optical axis for at least one pupil diameter in the range 3 mm to 5mm, over a spatial frequency range of 0 to 30 cycles/degree inclusive,at a wavelength selected from within the range 540 nm to 590 nminclusive.

(E5) A lens for an eye, the lens comprising: an optical axis; anaberration profile about the optical axis and having a focal distance;and at least two optical surfaces; and wherein the lens's opticalproperties can be characterised upon testing by at least the followingproperties: two or more higher order aberrations having one or more ofthe following components: a primary spherical aberration C(4,0), asecondary spherical aberration C(6,0), a tertiary spherical aberrationC(8,0), a quaternary spherical aberration C(10,0), a pentanary sphericalaberration C(12,0), a hexanary spherical aberration C(14,0), a heptanaryspherical aberration C(16,0), an octanary spherical aberration C(18,0)and a nanonary spherical aberration C(20,0); the aberration profile whentested on a model eye with no, or substantially no, aberrations andhaving an on-axis length equal, or substantially equal, to the focaldistance, results in a through focus RIQ, within the through focusrange, a first RIQ which is a peak RIQ and that remains at or above asecond RIQ over the through focus range that includes the focaldistance; and the first and second RIQs are measured for a model eyewith no, or substantially no, aberration and is measured along theoptical axis for at least one pupil diameter in the range 3 mm to 5 mm,over a spatial frequency range of 0 to 30 cycles/degree inclusive, at awavelength selected from within the range 540 nm to 590 nm inclusive.

(E6) A lens for an eye, the lens comprising: an optical axis; anaberration profile about the optical axis and having a focal distance;and at least two optical surfaces; and wherein the lens's opticalproperties can be characterised upon testing by at least the followingproperties: two or more higher order aberrations having one or more ofthe following components: a primary spherical aberration C(4,0), asecondary spherical aberration C(6,0), a tertiary spherical aberrationC(8,0), a quaternary spherical aberration C(10,0), a pentanary sphericalaberration C(12,0), a hexanary spherical aberration C(14,0), a heptanaryspherical aberration C(16,0), an octanary spherical aberration C(18,0)and a nanonary spherical aberration C(20,0); the aberration profile whentested on a model eye with no aberrations and having an on-axis lengthequal to the focal distance, results in a through focus RIQ, within thethrough focus range, a first RIQ which is a peak RIQ and that remains ator above a second RIQ over the through focus range that includes thefocal distance; and the first and second RIQs are measured for a modeleye with no aberration and is measured along the optical axis for atleast one pupil diameter in the range 3 mm to 5 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive, at a wavelengthselected from within the range 540 nm to 590 nm inclusive.

(E7) The lens of one or more of the above E examples, wherein thesingle-vision lens is one or more of the following: prescribed,appropriately prescribed, correctly prescribed and effectivelyprescribed.

(E8) The lens of one or more of the above E examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(E9) The lens of one or more of the above E examples, wherein the amountof light passing through the lens is at least 80%, 85%, 90%, 95% or 99%.

(E10) The lens of one or more of the above E examples, wherein thesingle-vision lens is a lens with a substantially constant power acrossa substantial portion of an optic zone of the single-vision lens.

(E11) The lens of one or more of the above E examples, wherein thesingle-vision lens is a lens with a constant power across a portion ofan optic zone of the single-vision lens.

(E12) The lens of one or more of the above E examples, wherein thesingle-vision lens is a lens with a substantially constant power acrossa portion of one or more optic zones of the single-vision lens.

(E13) The lens of one or more of the above E examples, wherein the lensis further characterised by minimal, substantially no or no, ghosting atnear, intermediate and far distances.

(E14) The lens of one or more of the above E examples, wherein the lensis further characterised by minimal, substantially no or no, ghosting atnear distances, intermediate distances and far distances.

(E15) The lens of one or more of the above E examples, wherein the lensis further configured to provide minimal, substantially no or no,ghosting at near, intermediate and far distances.

(E16) The lens of one or more of the above E examples, wherein theminimal ghosting is a lack of an undesired secondary image appearing atthe image plane of the optical system.

(E17) The lens of one or more of the above E examples, wherein theminimal ghosting is a lack of an undesired secondary image appearing onthe retina of the eye.

(E18) The lens of one or more of the above E examples, wherein theminimal ghosting is a lack of an undesired double image appearing on theretina of the eye.

(E19) The lens of one or more of the above E examples, wherein theminimal ghosting is a lack of false out-of-focus image appearing alongside of the primary image in an optical system.

(E20) The lens of one or more of the above E examples, wherein the lensis further configured to provide a sufficient lack of ghosting in aportion of near, intermediate and far distances.

(E21) The lens of one or more of the above E examples, wherein the lensis further configured to provide a sufficient lack of ghosting at neardistances, intermediate distances and far distances.

(E22) The lens of one or more of the above E examples, wherein the lensis further configured to provide a sufficient lack of ghosting in aportion of two or more of the following: near, intermediate and fardistances.

(E23) The lens of one or more of the above E examples, wherein lack ofghosting is lack of undesired image appearing at the image plane of theoptical system.

(E24) The lens of one or more of the above E examples, wherein lack ofghosting is a lack of false out of focus images appearing along side ofthe primary image in an optical system.

(E25) The lens of one or more of the above E examples, wherein the lensis further configured to provide a sufficient lack of ghosting in aportion of two or more of the following: near distances, intermediatedistances and far distances.

(E26) The lens of one or more of the above E examples, wherein the lensis further configured to provide the RIQ of at least 0.1, 0.13, 0.17,0.2, 0.225, or 0.25 in the near distance range, the RIQ of at least0.27, 0.3, 0.33, 0.35, 0.37 or 0.4 in the intermediate distance rangeand the RIQ of at least 0.35, 0.37, 0.4, 0.42, 0.45, 0.47, or 0.5 in thefar distance range.

(E27) The lens of one or more of the above E examples, wherein the lensis further configured to provide two or more of the following: the RIQof at least 0.1, 0.13, 0.17, 0.2, 0.225, or 0.25 in the near distancerange, the RIQ of at least 0.27, 0.3, 0.33, 0.35, 0.37 or 0.4 in theintermediate distance range and the RIQ of at least 0.35, 0.37, 0.4,0.42, 0.45, 0.47, or 0.5 in the far distance range.

(E28) The lens of one or more of the above E examples, wherein the RIQsare selected in the near, intermediate and far distance ranges such thatthe lens is configured to provide minimal, or no, ghosting in near,intermediate and far distances.

(E29) The lens of one or more of the above E examples, wherein the lensis configured to substantially eliminate, or substantially reduce,ghosting at near, intermediate and far distances.

(E30) The lens of one or more of the above E examples, wherein the lensis configured to substantially eliminate, or substantially reduce,ghosting at near distances, intermediate distances and far distances.

(E31) The lens of one or more of the above E examples, wherein neardistance is the range of 33 cm to 50 cm or 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm, 50 cm to 80 cm or 50 cm to 70cm; and far distance is the range of 100 cm or greater, 80 cm or greateror 70 cm or greater.

(E32) The lens of one or more of the above E examples, wherein neardistance is the range of 33 cm to 50 cm or 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm, 50 cm to 80 cm or 50 cm to 70cm; and far distance is the range of 100 cm or greater, 80 cm or greateror 70 cm or greater and the near, intermediate and far distances aredetermined by the distance from the object being focused on.

(E33) The lens of one or more of the above E examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm orgreater.

(E34) The lens of one or more of the above E examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm orgreater and the near, intermediate and far distances are determined bythe distance from the object being focused on.

(E35) The lens of one or more of the above E examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm tooptical infinity.

(E36) The lens of one or more of the above E examples, wherein neardistance is the range of 40 cm to 50 cm; intermediate distance is therange of 50 cm to 100 cm; and far distance is the range of 100 cm tooptical infinity and the near, intermediate and far distances aredetermined by the distance from the object being focused on.

(E37) The lens of one or more of the above E examples, wherein the lensis configured to minimize, or reduce, ghosting at near, intermediate andfar distances when used on an eye.

(E38) The lens of one or more of the above E examples, wherein the lensis configured to minimize, or reduce, ghosting at near distances,intermediate distances and far distances when used on an eye.

(E39) The lens of one or more of the above E examples, wherein the rangeof substantially continuous distances is continuous.

(E40) The lens of one or more of the above E examples, wherein the rangeof substantially continuous distances is continuous and goes from 40 cmto optical infinity.

(E41) The lens of one or more of the above E examples, wherein the rangeof substantially continuous distances is from 33 cm to optical infinity.

(E42) The lens of one or more of the above E examples, wherein the lensis configured such that at least 40%, 50%, 60% or 70% of a randomlyselected group of 15 affected individuals in the near distances,intermediate distances and far distances perceive minimal, or no,ghosting at near distances, intermediate distances and far distances.

(E43) The lens of one or more of the above E examples, wherein the lensis configured such that at least 60%, 70%, 80% or 90% of a randomlyselected group of 15 affected individuals in the intermediate distancesand far distances perceive minimal, or no, ghosting at intermediatedistances and far distances.

(E44) The lens of one or more of the above E examples, wherein thesingle vision lens provides a visual acuity for the user of one or moreof the following: at least 20/20, at least 20/30, at least 20/40, atleast about 20/20, at least about 20/30 and at least about 20/40, at farvisual distances.

(E45) The lens of one or more of the above E examples, wherein theaberration profile is comprised of a defocus term and at least two, twoor more, three, three or more, four, four or more, five, five or more,six, six or more, seven, seven or more, eight, eight or more, nine, nineor more, ten, or ten or more spherical aberration terms.

(E46) The lens of one or more of the above E examples, wherein theaberration profile is comprised of a defocus term and at least two,three, four, five, six, seven, eight, nine, or at least ten sphericalaberration terms.

(E47) The lens of one or more of the above E examples, wherein theaberration profile is comprised of a defocus term and sphericalaberration terms between C(4,0) and C(6,0), C(4,0) and C(8,0), C(4,0)and C(10,0), C(4,0) and C(12,0), C(4,0) and C(14,0), C(4,0) and C(16,0),C(4,0) and C(18,0) or C(4,0) and C(20,0).

(E48) The lens of one or more of the above E examples, wherein thesingle vision lens provides a visual acuity that is the best-correctedvisual acuity.

(E49) The lens of one or more of the above E examples, wherein thebest-corrected visual acuity is a visual acuity that cannot besubstantially improved by further manipulating the power of the singlevision lens.

(E50) The lens of one or more of the above E examples, wherein the lenshas two optical surfaces.

(E51) The lens of one or more of the above E examples, wherein the leastone aberration profile is along the optical axis of the lens.

(E52) The lens of one or more of the above E examples, wherein the lenshas a focal distance.

(E53) The lens of one or more of the above E examples, wherein theaberration profile includes higher order aberrations having at least oneof a primary spherical aberration component C(4,0) and a secondaryspherical aberration component C(6,0).

(E54) The lens of one or more of the above E examples, wherein the focaldistance is a prescription focal distance for a myopic, hyperopic,astigmatic, and/or presbyopic eye and wherein the focal distance differsfrom the focal distance for a C(2,0) Zernike coefficient of theaberration profile.

(E55) The lens of one or more of the above E examples, wherein thehigher order aberrations include at least two spherical aberration termsselected from the group C(4,0) to C(20,0).

(E56) The lens of one or more of the above E examples, wherein thehigher order aberrations include at least three spherical aberrationterms selected from the group C(4,0) to C(20,0).

(E57) The lens of one or more of the above E examples, wherein thehigher order aberrations include at least five spherical aberrationterms selected from the group C(4,0) to C(20,0).

(E58) The lens of one or more of the above E examples, wherein theaverage slope over a horizontal field of at least −20° to +20° degradesin a direction of eye growth.

(E59) The lens of one or more of the above E examples, wherein theaverage slope over a horizontal field of at least −20° to +20° improvesin a direction of eye growth.

(E60) The lens of one or more of the above E examples, wherein theaverage slope over a vertical field of at least −20° to +20° degrades ina direction of eye growth.

(E61) The lens of one or more of the above E examples, wherein theaverage slope over a vertical field of at least −20° to +20° improves ina direction of eye growth.

(E62) The lens of one or more of the above E examples, wherein the slopefor a substantial portion of the field angles over a horizontal field ofat least −20° to +20° degrades in a direction of eye growth.

(E63) The lens of one or more of the above E examples, wherein thesubstantial portion of the field angles over a horizontal field is atleast 75%, 85%, 95% or 99% of the field angles.

(E64) The lens of one or more of the above E examples, wherein thesubstantial portion of the field angles over a horizontal field is everyfield angle.

(E65) The lens of one or more of the above E examples, wherein the slopefor a substantial portion of the field angles over a vertical field ofat least −20° to +20° degrades in a direction of eye growth.

(E66) The lens of one or more of the above E examples, wherein thesubstantial portion of the field angles over a vertical field is everyangle.

(E67) The lens of one or more of the above E examples, wherein thesubstantial portion of the field angles over a vertical field is atleast 75%, 85%, 95% or 99% of the field angles.

(E68) The lens of one or more of the above E examples, wherein theaberration profile provides the RIQ of at least 0.3 at the focal lengthfor a substantial portion of pupil diameters in the range 3 mm to 6 mm.

(E69) The lens of one or more of the above E examples, wherein theaberration profile provides the RIQ of at least 0.3 at the focal lengthfor a substantial portion of pupil diameters in the range 4 mm to 5 mm.

(E70) The lens of one or more of the above E examples, wherein theaberration profile provides the RIQ with a through focus slope thatdegrades in a direction of eye growth when primary or secondaryastigmatism is added to the aberration profile.

(E71) The lens of one or more of the above E examples, wherein theaberration profile provides the RIQ with a through focus slope thatimproves in a direction of eye growth when primary or secondaryastigmatism is added to the aberration profile.

(E72) The lens of one or more of the above E examples, wherein theprimary or secondary astigmatism is added to the desired aberrationprofile by altering one or more of the following terms: C(2,−2), C(2,2),C(4,−2), C(4,2), C(6,−2) and/or C(6,2).

(E73) The lens of one or more of the above E examples, wherein theaberration profile provides the RIQ with a through focus slope thatdegrades in a direction of eye growth when secondary astigmatism isadded to the aberration profile.

(E74) The lens of one or more of the above E examples, wherein thesecondary astigmatism is added to the desired aberration profile byaltering one or more of the following terms: C(2,−2), C(2,2), C(4,−2),C(4,2), C(6,−2) and/or C(6,2).

(E75) The lens of one or more of the above E examples, wherein the RIQis characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity function CSF(F)=2.6(0.0192+0.114f)e^(−(0.114t)̂1.1), where f specifies the testedspatial frequency, in the range of F_(min) to F_(max); FT denotes a 2Dfast Fourier transform;A (ρ, θ) denotes the pupil amplitude function across the pupil diameter;W (ρ, θ) denotes wavefront of the test case measured for i=1 to 20

W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ);

Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(E76) The lens of one or more of the above E examples, wherein the RIQis characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity function CSF(F)=2.6(0.0192+0.114f)e^(−(0.114t)̂1.1), where f specifies the testedspatial frequency, in the range of F_(min) to F_(max);FT denotes a 2D Fourier transform, for example a 2D fast Fouriertransform;A (ρ, θ) denotes the pupil amplitude function across the pupil diameter;W (ρ, θ) denotes wavefront of the test case measured for i=1 to k;wherein k is a positive integer;

W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ);

Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(E77) The lens of one or more of the above E examples, wherein the firstvisual Strehl Ratio is at least 0.3, 0.35, 0.4, 0.5, 0.6, 0.7 or 0.8.

(E78) The lens of one or more of the above E examples, wherein thesecond visual Strehl Ratio is at least 0.1, 0.12, 0.15, 0.18 or 0.2.

(E79) The lens of one or more of the above E examples, wherein thethrough focus range is at least 1.7, 1.8, 1.9, 2, 2.1, 2.25 or 2.5Dioptres.

(E80) The lens of one or more of the above E examples, wherein the lenshas a prescription focal distance located within 0.75, 0.5, 0.3, or 0.25Dioptres, inclusive, of an end of the through focus range.

(E81) The lens of one or more of the above E examples, wherein the endof the through focus range is the negative power end.

(E82) The lens of one or more of the above E examples, wherein the endof the through focus range is the positive power end.

(E83) The lens of one or more of the above E examples, wherein thevisual Strehl Ratio remains at or above the second visual Strehl Ratioover the through focus range and over a range of pupil diameters of atleast 1 mm, 1.5 mm, 2 mm, 2.5 mm or 3 mm.

(E84) The lens of one or more of the above E examples, wherein thecombination of higher order aberrations includes at least one of primaryspherical aberration and secondary spherical aberration.

(E85) The lens of one or more of the above E examples, wherein thehigher order aberrations include at least two, three, or five sphericalaberration terms selected from the group C(4,0) to C(20,0).

(E86) The lens of one or more of the above E examples, wherein thehigher order aberrations include at least six, seven or eight sphericalaberration terms selected from the group C(4,0) to C(20,0).

(E87) The lens of one or more of the above E examples, wherein theaberration profile is capable of being characterised using onlyspherical aberration Zernike coefficients C (4, 0) to C (20, 0).

(E88) The lens of one or more of the above E examples, wherein the RIQfor a substantial portion of the angles over a horizontal field of atleast −10° to +10°, −20° to +20° or −30° to +30° is at least 0.3, 0.35or 0.4.

(E89) The lens of one or more of the above E examples, wherein the RIQfor a substantial portion of the angles over a vertical field of atleast −10° to +10°, −20° to +20° or −30° to +30° is at least 0.3, 0.35or 0.4.

(E90) The lens of one or more of the above E examples, wherein the RIQfor a substantial portion of the angles over a horizontal field of atleast −10° to +10°, −20° to +20° or −30° to +30° is at least 0.3.

(E91) The lens of one or more of the above E examples, wherein the lensis one or more of the following: contact lens, corneal onlays, cornealinlays, anterior chamber intraocular lens or posterior chamberintraocular lens.

(E92) The lens of one or more of the above E examples, wherein the RIQfor a substantial portion of the angles over a vertical field of atleast −10° to +10°, −20° to +20° or −30° to +30° is at least 0.3.

(E93) The lens of one or more of the above E examples, wherein the lensis one of the following: contact lens, corneal onlays, corneal inlays,anterior chamber intraocular lens or posterior chamber intraocular lens.

(E94) The lens of one or more of the above E examples, wherein a firstlens is provided based on one or more of the E examples and a secondlens is provided based on one or more of the E examples to form a pairof lenses.

(E95) The lens of one or more of the above E examples, wherein the firstlens is provided based on one or more of the E examples and a secondlens is provided to form a pair of lenses.

(E96) The lens of one or more of the above E examples, wherein a pair oflenses are provided for use by an individual to substantially correctthe individual's vision.

(E97) The lens of one or more of the above E examples, wherein the slopeaveraged over a horizontal field of at least −20° to +20° degrades in adirection of eye growth.

(E98) The lens of one or more of the above E examples, wherein the slopeaveraged over a horizontal field of at least −20° to +20° improves in adirection of eye growth.

(E99) The lens of one or more of the above E examples, wherein the slopeaveraged over a vertical field of at least −20° to +20° degrades in adirection of eye growth.

(E100) The lens of one or more of the above E examples, wherein theslope averaged over a vertical field of at least −20° to +20° improvesin a direction of eye growth.

(E101) A method for making or using one or more of the lenses of one ormore of the above E examples.

(E102) A lens of one or more of the above E examples, wherein a powerprofile is associated with the optical axis and the power profile has atransition between a maxima and a minima, and the maxima is within 0.2mm of the centre of the optic zone and the minima is less than or equalto 0.3, 0.6, 0.9 or 1 mm distance from the maxima; wherein the amplitudeof the transition between the maxima and the minima is at least 2.5D,4D, 5D, or 6D.

(E103) The lens of one of the claims E, wherein the transition betweenthe maxima and the minima is one or more of the following: continuous,discontinuous, monotonic and non-monotonic.

Examples Set F

(F1) A lens comprising: an optical axis; an aberration profile about theoptical axis and having a focal distance; at least two optical surfaces;an aperture size greater than 2 mm; wherein the lens is configured suchthat the lens is characterised by one or more power profiles and the oneor more power profiles provide a lens that has the following properties:the visual performance of the multifocal lens at near, intermediate andfar visual distances is substantially equivalent to or better than anappropriately prescribed single-vision lens for far visual distance andproduces minimal ghosting at distances from far distance to near.

(F2) A lens comprising: an optical axis; an aberration profile having afocal distance; and at least two optical surfaces; wherein the lens isconfigured at least in part by one or more power profiles and the lenshas the following properties: the visual performance of the lens atnear, intermediate and far visual distances is substantially equivalentto, or better than, an appropriately prescribed single-vision lens forfar visual distance and produces minimal ghosting at distances from fardistance to near.

(F3) A lens comprising: an optical axis; an aberration profile having afocal distance; at least two optical surfaces; wherein the lens isconfigured at least in part by one or more power profiles and the lenshas the following properties: the visual performance of the lens atintermediate and far visual distances is substantially equivalent to, orbetter than, a properly prescribed single-vision lens for far visualdistance and produces minimal ghosting at distances from far distance tonear.

(F4) A lens comprising: an optical axis; an aberration profile having afocal distance; at least two optical surfaces; the lens is configured byone or more power profiles and has the following lens properties: thelens is capable of decreasing the rate of progression of myopia; thelens is capable of decreasing the rate of growth of the eye as measuredby axial length; and provides visual performance at intermediate and farvisual distances that is at least substantially equivalent to a properlyprescribed single-vision lens for far visual distance and producesminimal ghosting at distances from far distance to near.

(F5) A lens comprising: an optical axis; at least two optical surfaces;an aberration profile having a focal distance and/or at least one powerprofile, wherein the aberration profile and/or at least one powerprofile configure the lens to provide an image profile and the imageprofile in use with an eye is capable of stabilising and/or altering thegrowth of the eye; and wherein the lens is configured to provide visualperformance at intermediate and far visual distances that issubstantially equivalent to or better than a correctly prescribedsingle-vision lens for far visual distance and produces minimal ghostingat distances from far distance to near; wherein the image profilegenerates one or more of the following: myopic and/or hyperopic defocusat centre and/or periphery of the retina; a RIQ of at least 0.3, 0.35 or0.4 at the retina and a slope of through-focus RIQ that degrades in thedirection of eye growth; and a RIQ of at least 0.3, 0.35 or 0.4 at theretina and a slope of through-focus RIQ that improves in the directionof eye growth.

(F6) The lens of one or more of the above F examples, wherein the imageprofile created by the lens has the effect of slowing the growth of themyopic eye by one or more stop signals.

(F7) The lens of one or more of the above F examples, wherein the slopeof through-focus RIQ that degrades in the direction of eye growth is oneor more of the following: substantial, partial, sufficient orcombinations thereof,

(F8) The lens of one or more of the above F examples, myopia controllens.

(F9) The lens of one or more of the above F examples, wherein theimprovement in the direction of growth is one or more of the following:substantial, partial, sufficient or combinations thereof.

(F10) The lens of one or more of the above F examples, wherein the lenshas an aperture size of 2 mm or greater; 2.5 mm or greater, 3 mm orgreater, 3.5 mm or greater or 4 mm or greater.

(F11) The lens of one or more of the above F examples, wherein the lensis a multifocal lens with at least 1 Dioptre, at least 1.25 Dioptre, orat least 1.5 Dioptre of power variation across a central and/or amid-peripheral portion of the optical zone of the lens.

(F12) The lens of one or more of the above F examples, wherein the lensis a presbyopic multifocal lens with at least 1 Dioptre, at least 1.25Dioptre or at least 1 Dioptre of power variation across a central and/ora mid-peripheral portion of the optical zone of the lens.

(F13) The lens of one or more of the above F examples, wherein the lensis non-monotonic and non-periodic.

(F14) The lens of one or more of the above F examples, wherein the lensis a non-pinhole lens.

(F15) The lens of one or more of the above F examples, wherein the lensis a non-pinhole lens and the lens is a multifocal lens with at least 1,1.25 or 1.5 Dioptre of power variation across a central and/or amid-peripheral portion of the optical zone of the lens.

(F16) The lens of one or more of the above F examples, wherein in thelens produces a retinal image quality (RIQ) with a through focus slopethat degrades in a direction of eye growth, where the RIQ is determinedby a visual Strehl Ratio that is measured substantially along theoptical axis when the aberration profile is tested on a model eye withno or substantially no aberrations and having an on-axis length equal orsubstantially equal to the focal distance.

(F17) The lens of one or more of the above F examples, wherein in thelens produces a retinal image quality (RIQ) with a through focus slopethat degrades in a direction of eye growth, where the RIQ is determinedby a visual Strehl Ratio that is measured along the optical axis whenthe aberration profile is tested on a model eye with no aberrations andhaving an on-axis length equal to the focal distance.

(F18) The lens of one or more of the above F examples, wherein the lenshas at least one wavefront aberration profile associated with theoptical axis, and the aberration profile is comprised of: at least twospherical aberration selected at least in part from a group comprisingZernike coefficients C(4,0) to C(20,0).

(F19) The lens of one or more of the above F examples, wherein the lenscan be characterised upon testing by at least the following properties:two or more higher order aberrations having one or more of the followingcomponents: a primary spherical aberration C(4,0), a secondary sphericalaberration (C(6,0), a tertiary spherical aberration C(8,0), a quaternaryspherical aberration C(10,0), a pentanary spherical aberration C(12,0),a hexanary spherical aberration C(14,0), a heptanary sphericalaberration C(16,0), an octanary spherical aberration C(18,0) and ananonary spherical aberration C(20,0).

(F20) The lens of one or more of the above F examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(F21) The lens of one or more of the above F examples, wherein theamount of light passing through the lens is at least 80%, 85%, 90%, 95%or 99%.

Examples Set G

(G1) A multifocal lens comprising: an optical axis; the multifocal lensis configured based on an aberration profile associated with the opticalaxis; the aberration profile is comprised of at least two sphericalaberration terms and a defocus term; the multifocal lens is configuredsuch that the visual performance of the multifocal lens at intermediateand far visual distances is substantially equivalent to, or better than,an appropriately or properly prescribed single-vision lens for farvisual distance; and when tested with a defined visual rating scale of 1to 10 units, the visual performance at the near visual distance iswithin two units of the visual performance of the appropriatelyprescribed single-vision lens at far distance.

(G2) A multifocal lens comprising: an optical axis; the multifocal lensis configured in part on an aberration profile associated with theoptical axis; the aberration profile is comprised of at least twospherical aberration terms and a defocus term; wherein the multifocallens is configured such that the visual performance of the multifocallens at intermediate and far visual distances is equivalent to or betterthan, an appropriately or correctly prescribed single-vision lens forfar visual distance; and wherein upon testing with a defined visualrating scale of 1 to 10 units, the visual performance at the near visualdistance is within two units of the visual performance of the correctlyprescribed single-vision lens at far distance.

(G3) A multifocal lens comprising: an optical axis; the multifocal lensis configured based on an aberration profile associated with the opticalaxis; the aberration profile is comprised of at least two sphericalaberration terms and a defocus term; and wherein upon testing with adefined overall visual rating scale of 1 to 10 units, the multifocallens is configured such that the overall visual performance of themultifocal lens is substantially equivalent to or better than anappropriately prescribed single-vision lens for far visual distance.

(G4) A multifocal lens comprising: an optical axis; the multifocal lensis configured based in part on an aberration profile associated with theoptical axis; the aberration profile is comprised of at least twospherical aberration terms and a defocus term; and wherein themultifocal lens is configured such that the visual performance on avisual analogue scale, with the multifocal lens, at far visual distance,has a score of 9 or above in 55%, 60%, 65%, 70%, 75% or 80% of arepresentative sample of presbyopes; wherein the multifocal lens isconfigured such that the visual performance on a visual analogue scale,with the multifocal lens, at intermediate visual distance, has a scoreof 9 or above in 45%, 50%, 55%, 60%, 65%, 70% or 75% of a representativesample of presbyopes; and wherein the multifocal lens is configured suchthat the visual performance on a visual analogue scale, with themultifocal lens, at near visual distance has a score of 9 or above in25%, 30%, 35%, 40%, 45%, 50% or 55% of a representative sample ofpresbyopes.

(G5) A multifocal lens comprising: an optical axis; the multifocal lensbeing characterised or configured in part on an aberration profileassociated with the optical axis; the aberration profile is comprised ofat least two spherical aberration terms and a defocus term; and whereinthe multifocal lens is configured such that the overall visualperformance on a visual analogue scale results in a score of 9 or abovein 18%, 25%, 30%, 35%, 40% or 45% of a representative sample ofpresbyopes.

(G6) The multifocal lens of one or more of the above G examples, whereinthe multifocal lens in use provides substantially minimal ghosting tothe vision of the user at near and far visual distances.

(G7) The multifocal lens of one or more of the above G examples, whereinthe substantially equivalent to or better visual performance isdetermined at least in part by a visual rating scale of 1 to 10 units.

(G8) The multifocal lens of one or more of the above G examples, whereinthe average visual performance of the lens in use for a representativesample of the affected population has a distance vision score of atleast 8.5, has an intermediate vision score of at least 8.5 and has anear vision score of at least 7.5.

(G9) The multifocal lens of one or more of the above G examples, whereinthe average visual performance of the lens in use for a representativesample of the affected population has a distance vision score of atleast 8.0, at least 8.2 or at least 8.4; has an intermediate visionscore of at least 8.0, at least 8.2 or at least 8.4; has a near visionscore of at least 7.0, at least 7.2 or at least 7.4; or combinationsthereof.

(G10) The multifocal lens of one or more of the above G examples,wherein the multifocal lens provides substantially minimal ghosting fora representative sample of the affected population at near and/orintermediate visual distances.

(G11) The multifocal lens of one or more of the above G examples,wherein substantial minimal ghosting is an average visual performancescore of less than or equal to 2.4, 2.2, 2, 1.8, 1.6 or 1.4 on thevision analogue ghosting scale of 1 to 10 units for a representativesample of the affected population using the multifocal lens.

(G12) The multifocal lens of one or more of the above G example, whereinsubstantial minimal ghosting is a score of less than or equal to 2.4,2.2, 2, 1.8, 1.6 or 1.4 on the vision rating ghosting scale 1 to 10units utilising the average visual performance of the lens in use on asample of people needing vision correction and/or therapy, for one ormore of the following: myopia, hyperopia, astigmatism, emmetropia andpresbyopia.

(G13) The multifocal lens of one or more of the above G examples,wherein the lens provides myopia control therapy with minimal ghostingwith or without vision correction.

(G14) The multifocal lens of one or more of the above G examples,wherein the lens provides presbyopia correction with minimal ghostingwith or without far vision correction.

(G15) The multifocal lens of one or more of the above G examples,wherein the lens corrects astigmatism up to 1 Dioptre withoutsubstantial use of rotationally stable toric lens design features.

(G16) The multifocal lens of one or more of the above G examples,wherein the lens corrects astigmatism up to 1 Dioptre withoutsubstantial use of rotationally stable toric lens design features withminimal ghosting.

(G17) The multifocal lens of one or more of the above G examples,further comprising a first lens and a second lens wherein the first lensis biased to substantially optimise distance vision and the second lensis biased to substantially optimise near vision, and when used togetherprovide monocular and binocular vision substantially equivalent to, orbetter than, an appropriately prescribed single-vision lens for farvisual distance, wherein the pair of lenses provide stereopsis withminimal ghosting.

(G18) The multifocal lens of one or more of the above G examples,wherein the average overall visual performance of the lens in use for arepresentative sample of the affected population has an overall visionscore of at least 7.8, 8, 8.2, 8.4, 8.6, 8.8 or 9.

(G19) The multifocal lens of one or more of the above G examples,wherein the average overall visual performance of the lens in use for arepresentative sample of the affected population has an overall visionscore of at least 7.8, 8, 8.2, 8.4, 8.6, 8.8 or 9.

(G20) The multifocal lens of one or more of the above G examples,wherein the multifocal lens in use provides substantially minimalghosting to the vision of the user at near and far visual distances.

(G21) The multifocal lens of one or more of the above G examples,wherein the substantially equivalent to or better visual performance isdetermined at least in part by a visual rating scale of 1 to 10 units.

(G22) The multifocal lens of one or more of the above G examples,wherein the substantially equivalent to or better visual performance issubstantially determined by a visual rating scale of 1 to 10 units.

(G23) The multifocal lens of one or more of the above G examples,wherein the average visual performance of the lens in use for arepresentative sample of the affected population has a distance visionscore of at least 8.5, has an intermediate vision score of at least 8.5and has a near vision score of at least 7.5.

(G24) The multifocal lens of one or more of the above G examples,wherein the average visual performance of the lens in use for arepresentative sample of the affected population has a distance visionscore of at least 8.0, at least 8.2 or at least 8.4; has an intermediatevision score of at least 8.0, at least 8.2 or at least 8.4; has a nearvision score of at least 7.0, at least 7.2 or at least 7.4, orcombinations thereof.

(G25) The multifocal lens of one or more of the above G examples,wherein the multifocal lens in use provides the average visualperformance of the lens in use for a representative sample of theaffected population provide substantially minimal ghosting to the visionof the user at near and/or intermediate visual distances.

(G26) The multifocal lens of one or more of the above G examples,wherein substantial minimal ghosting is defined as a score of less thanor equal to 2.5, 2.2, 2, 1.8, 1.6 or 1.4 on the vision rating ghostingscale 1 to 10 units utilising the average visual performance of the lensin use for a representative sample of the affected population.

(G27) The multifocal lens of one or more of the above G examples,wherein the average overall visual performance of the lens in use for arepresentative sample of the affected population has an overall visionscore of at least 7.8, 8, 8.2, 8.4, 8.6, 8.8 or 9.

(G28) The multifocal lens of one or more of the above G examples,wherein the single-vision lens is a lens with a substantially constantpower across a substantial portion of an optic zone of the single-visionlens.

(G29) The multifocal lens of one or more of the above G examples,wherein the lens is used for a presbyopic eye.

(G30) The multifocal lens of one or more of the above G examples,wherein the lens is further characterised by minimal, or no, ghosting atnear, intermediate and far distances.

(G31) The multifocal lens of one or more of the above G examples, wherein the substantially continuous distances is continuous.

(G32) The multifocal lens of one or more of the above G examples,wherein the single-vision lens is one or more of the following:prescribed, appropriately prescribed, correctly prescribed andeffectively prescribed.

(G33) The multifocal lens of one or more of the above G examples,wherein the single-vision lens is a lens with a substantially constantpower across a substantial portion of an optic zone of the single-visionlens.

(G34) The multifocal lens of one or more of the above G examples,wherein the single-vision lens is a lens with a constant power across aportion of an optic zone of the single-vision lens.

(G35) The multifocal lens of one or more of the above G examples,wherein the single-vision lens is a lens with a substantially constantpower across a portion of one or more optic zones of the single-visionlens.

(G36) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is used for a presbyopic eye.

(G37) The multifocal lens of one or more of the above G examples,wherein the lens is configured for a presbyopic eye.

(G38) The multifocal lens of one or more of the above G examples,wherein the lens is configured to optically correct or substantiallycorrect presbyopia.

(G39) The multifocal lens of one or more of the above G examples,wherein the lens is configured to mitigate or substantially mitigate theoptical consequences of presbyopia.

(G40) The multifocal lens of one or more of the above G examples,wherein the lens is configured to alter or substantially alter apresbyopic condition to a non-presbyopic condition.

(G41) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is used for at least correcting a presbyopiceye condition and when used provides an appropriate correction to adjustthe vision of the user towards substantially normal non-presbyopicvision.

(G42) The multifocal lens of one or more of the above G examples,wherein normal vision is 6/6 or better.

(G43) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further characterised by minimal,substantially no or no, ghosting at near, intermediate and fardistances.

(G44) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further characterised by minimal,substantially no or no, ghosting at near distances, intermediatedistances and far distances.

(G45) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further configured to provide minimal,substantially no or no, ghosting at near, intermediate and fardistances.

(G46) The multifocal lens of one or more of the above G examples,wherein the minimal ghosting is a lack of an undesired secondary imageappearing at the image plane of the optical system.

(G47) The multifocal lens of one or more of the above G examples,wherein the minimal ghosting is a lack of an undesired secondary imageappearing on the retina of the eye.

(G48) The multifocal lens of one or more of the above G examples,wherein the minimal ghosting is a lack of an undesired double imageappearing on the retina of the eye.

(G49) The multifocal lens of one or more of the above G examples,wherein the minimal ghosting is a lack of false out-of-focus imageappearing along side of the primary image in an optical system.

(G50) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further configured to provide asufficient lack of ghosting in a portion of near, intermediate and fardistances.

(G51) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further configured to provide asufficient lack of ghosting at near distances, intermediate distancesand far distances.

(G52) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further configured to provide asufficient lack of ghosting in a portion of two or more of thefollowing: near, intermediate and far distances.

(G53) The multifocal lens of one or more of the above G examples,wherein lack of ghosting is lack of undesired image appearing at theimage plane of the optical system.

(G54) The multifocal lens of one or more of the above G examples,wherein lack of ghosting is a lack of false out of focus imagesappearing along side of the primary image in an optical system.

(G55) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further configured to provide asufficient lack of ghosting in a portion of two or more of thefollowing: near distances, intermediate distances and far distances.

(G56) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further configured to provide the RIQ ofat least 0.1, 0.13, 0.17, 0.2, 0.225, or 0.25 in the near distancerange, the RIQ of at least 0.27, 0.3, 0.33, 0.35, 0.37 or 0.4 in theintermediate distance range and the RIQ of at least 0.35, 0.37, 0.4,0.42, 0.45, 0.47, or 0.5 in the far distance range.

(G57) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is further configured to provide two or moreof the following: the RIQ of at least 0.1, 0.13, 0.17, 0.2, 0.225, or0.25 in the near distance range, the RIQ of at least 0.27, 0.3, 0.33,0.35, 0.37 or 0.4 in the intermediate distance range and the RIQ of atleast 0.35, 0.37, 0.4, 0.42, 0.45, 0.47, or 0.5 in the far distancerange.

(G58) The multifocal lens of one or more of the above G examples,wherein the RIQs are selected in the near, intermediate and far distanceranges such that the multifocal lens is configured to provide minimal,or no, ghosting in near, intermediate and far distances.

(G59) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is configured to substantially eliminate, orsubstantially reduce, ghosting at near, intermediate and far distances.

(G60) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is configured to substantially eliminate, orsubstantially reduce, ghosting at near distances, intermediate distancesand far distances.

(G61) The multifocal lens of one or more of the above G examples,wherein near distance is the range of 33 cm to 50 cm or 40 cm to 50 cm;intermediate distance is the range of 50 cm to 100 cm, 50 cm to 80 cm or50 cm to 70 cm; and far distance is the range of 100 cm or greater, 80cm or greater or 70 cm or greater.

(G62) The multifocal lens of one or more of the above G examples,wherein near distance is the range of 33 cm to 50 cm or 40 cm to 50 cm;intermediate distance is the range of 50 cm to 100 cm, 50 cm to 80 cm or50 cm to 70 cm; and far distance is the range of 100 cm or greater, 80cm or greater or 70 cm or greater and the near, intermediate and fardistances are determined by the distance from the object being focusedon.

(G63) The multifocal lens of one or more of the above G examples,wherein near distance is the range of 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm; and far distance is the rangeof 100 cm or greater.

(G64) The multifocal lens of one or more of the above G examples,wherein near distance is the range of 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm; and far distance is the rangeof 100 cm or greater and the near, intermediate and far distances aredetermined by the distance from the object being focused on.

(G65) The multifocal lens of one or more of the above G examples,wherein near distance is the range of 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm; and far distance is the rangeof 100 cm to optical infinity.

(G66) The multifocal lens of one or more of the above G examples,wherein near distance is the range of 40 cm to 50 cm; intermediatedistance is the range of 50 cm to 100 cm; and far distance is the rangeof 100 cm to optical infinity and the near, intermediate and fardistances are determined by the distance from the object being focusedon.

(G67) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is configured to minimize, or reduce,ghosting at near, intermediate and far distances when used on an eye.

(G68) The multifocal lens of one or more of the above G examples,wherein the multifocal lens is configured to minimize, or reduce,ghosting at near distances, intermediate distances and far distanceswhen used on an eye.

(G69) The multifocal lens of one or more of the above G examples,wherein the range of substantially continuous distances is continuous.

(G70) The multifocal lens of one or more of the above G examples,wherein the range of substantially continuous distances is continuousand goes from 40 cm to optical infinity.

(G71) The multifocal lens of one or more of the above G examples,wherein the range of substantially continuous distances is from 33 cm tooptical infinity.

(G72) The multifocal lens of one or more of the above G examples,wherein the lens is configured such that at least 40%, 50%, 60% or 70%of a randomly selected group of 15 affected individuals in the neardistances, intermediate distances and far distances perceive minimal, orno, ghosting at near distances, intermediate distances and fardistances.

(G73) The multifocal lens of one or more of the above G examples,wherein the lens is configured such that at least 60%, 70%, 80% or 90%of a randomly selected group of 15 affected individuals in theintermediate distances and far distances perceive minimal, or no,ghosting at intermediate distances and far distances.

(G74) The multifocal lens of one or more of the above G examples,wherein the single vision lens provides a visual acuity for the user ofone or more of the following: at least 20/20, at least 20/30, at least20/40, at least about 20/20, at least about 20/30 and at least about20/40, at far visual distances.

(G75) The multifocal lens of one or more of the above G examples,wherein the aberration profile is comprised of a defocus term and atleast two, two or more, three, three or more, four, four or more, five,five or more, six, six or more, seven, seven or more, eight, eight ormore, nine, nine or more, ten, or ten or more spherical aberrationterms.

(G76) The multifocal lens of one or more of the above G examples,wherein the aberration profile is comprised of a defocus term and atleast two, three, four, five, six, seven, eight, nine, or at least tenspherical aberration terms.

(G77) The multifocal lens of one or more of the above G examples,wherein the aberration profile is comprised of a defocus term andspherical aberration terms between C(4,0) and C(6,0), C(4,0) and C(8,0),C(4,0) and C(10,0), C(4,0) and C(12,0), C(4,0) and C(14,0), C(4,0) andC(16,0), C(4,0) and C(18,0), or C(4,0) and C(20,0).

(G78) The multifocal lens of one or more of the above G examples,wherein the single vision lens provides a visual acuity that is thebest-corrected visual acuity.

(G79) The multifocal lens of one or more of the above G examples,wherein the best-corrected visual acuity is a visual acuity that cannotbe substantially improved by further manipulating the power of thesingle vision lens.

(G80) The multifocal lens of one or more of the above G examples,wherein the lens has two optical surfaces.

(G81) The multifocal lens of one or more of the above G examples,wherein the least one aberration profile is along the optical axis ofthe lens.

(G82) The multifocal lens of one or more of the above G examples,wherein the lens has a focal distance.

(G83) The multifocal lens of one or more of the above G examples,wherein the aberration profile includes higher order aberrations havingat least one of a primary spherical aberration component C(4,0) and asecondary spherical aberration component C(6,0).

(G84) The multifocal lens of one or more of the above G examples,wherein the aberration profile provides, for a model eye with no, orsubstantially no, aberrations and an on-axis length equal to the focaldistance: the retinal image quality (RIQ) with a through focus slopethat degrades in a direction of eye growth; and the RIQ of at least 0.3;wherein the RIQ is visual Strehl Ratio measured along the optical axisfor at least one pupil diameter in the range 3 mm to 6 mm, over aspatial frequency range of 0 to 30 cycles/degree inclusive and at awavelength selected from within the range 540 nm to 590 nm inclusive.

(G85) The multifocal lens of one or more of the above G examples,wherein the aberration profile provides, for a model eye with no, orsubstantially no, aberrations and an on-axis length equal to the focaldistance: the retinal image quality (RIQ) with a through focus slopethat improves in a direction of eye growth; and the RIQ of at least 0.3;wherein the RIQ is visual Strehl Ratio measured along the optical axisfor at least one pupil diameter in the range 3 mm to 6 mm, over aspatial frequency range of 0 to 30 cycles/degree inclusive and at awavelength selected from within the range 540 nm to 590 nm inclusive.

(G86) The multifocal lens of one or more of the above G examples,wherein the lens has an optical axis and an aberration profile about itsoptical axis, the aberration profile: having a focal distance; andincluding higher order aberrations having at least one of a primaryspherical aberration component C(4,0) and a secondary sphericalaberration component C(6,0), wherein the aberration profile provides,for a model eye with no, or substantially no, aberrations and an on-axislength equal, or substantially equal, to the focal distance: the RIQwith a through focus slope that degrades in a direction of eye growth;and the RIQ of at least 0.3; wherein the RIQ is visual Strehl Ratiomeasured along the optical axis for at least one pupil diameter in therange 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(G87) The multifocal lens of one or more of the above G examples,wherein the lens has an optical axis and an aberration profile about itsoptical axis, the aberration profile: having a focal distance; andincluding higher order aberrations having at least one of a primaryspherical aberration component C(4,0) and a secondary sphericalaberration component C(6,0), wherein the aberration profile provides,for a model eye with no, or substantially no, aberrations and an on-axislength equal, or substantially equal, to the focal distance: the RIQwith a through focus slope that improves in a direction of eye growth;and the RIQ of at least 0.3; wherein the RIQ is visual Strehl Ratiomeasured along the optical axis for at least one pupil diameter in therange 3 mm to 6 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive and at a wavelength selected from within therange 540 nm to 590 nm inclusive.

(G88) The multifocal lens of one or more of the above G examples,wherein the focal distance is a prescription focal distance for amyopic, hyperopic, astigmatic, and/or presbyopic eye and wherein thefocal distance differs from the focal distance for a C(2,0) Zernikecoefficient of the aberration profile.

(G89) The multifocal lens of one or more of the above G examples,wherein the higher order aberrations include at least two sphericalaberration terms selected from the group C(4,0) to C(20,0).

(G90) The multifocal lens of one or more of the above G examples,wherein the higher order aberrations include at least three sphericalaberration terms selected from the group C(4,0) to C(20,0).

(G91) The multifocal lens of one or more of the above G examples,wherein the higher order aberrations include at least five sphericalaberration terms selected from the group C(4,0) to C(20,0).

(G92) The multifocal lens of one or more of the above G examples,wherein the average slope over a horizontal field of at least −20° to+20° degrades in a direction of eye growth.

(G93) The multifocal lens of one or more of the above G examples,wherein the average slope over a horizontal field of at least −20° to+20° improves in a direction of eye growth.

(G94) The multifocal lens of one or more of the above G examples,wherein the average slope over a vertical field of at least −20° to +20°degrades in a direction of eye growth.

(G95) The multifocal lens of one or more of the above G examples,wherein the average slope over a vertical field of at least −20° to +20°improves in a direction of eye growth.

(G96) The multifocal lens of one or more of the above G examples,wherein the slope for a substantial portion of the field angles over ahorizontal field of at least −20° to +20° degrades in a direction of eyegrowth.

(G97) The multifocal lens of one or more of the above G examples,wherein the substantial portion of the field angles over a horizontalfield is at least 75%, 85%, 95% or 99% of the field angles.

(G98) The multifocal lens of one or more of the above G examples,wherein the substantial portion of the field angles over a horizontalfield is every field angle.

(G99) The multifocal lens of one or more of the above G examples,wherein the slope for a substantial portion of the field angles over avertical field of at least −20° to +20° degrades in a direction of eyegrowth.

(G100) The multifocal lens of one or more of the above G examples,wherein the substantial portion of the field angles over a verticalfield is every angle.

(G101) The multifocal lens of one or more of the above G examples,wherein the substantial portion of the field angles over a verticalfield is at least 75%, 85%, 95% or 99% of the field angles.

(G102) The multifocal lens of one or more of the above G examples,wherein the aberration profile provides the RIQ of at least 0.3 at thefocal length for a substantial portion of pupil diameters in the range 3mm to 6 mm.

(G103) The multifocal lens of one or more of the above G examples,wherein the aberration profile provides the RIQ of at least 0.3 at thefocal length for a substantial portion of pupil diameters in the range 4mm to 5 mm.

(G104) The multifocal lens of one or more of the above G examples,wherein the aberration profile provides the RIQ with a through focusslope that degrades in a direction of eye growth when primary orsecondary astigmatism is added to the aberration profile.

(G105) The multifocal lens of one or more of the above G examples,wherein the aberration profile provides the RIQ with a through focusslope that improves in a direction of eye growth when primary orsecondary astigmatism is added to the aberration profile.

(G106) The multifocal lens of one or more of the above G examples,wherein the primary or secondary astigmatism is added to the desiredaberration profile by altering one or more of the following terms:C(2,−2), C(2,2), C(4,−2), C(4,2), C(6,−2), and/or C(6,2).

(G107) The multifocal lens of one or more of the above G examples,wherein the aberration profile provides the RIQ with a through focusslope that degrades in a direction of eye growth when secondaryastigmatism is added to the aberration profile.

(G108) The multifocal lens of one or more of the above G examples,wherein the secondary astigmatism is added to the desired aberrationprofile by altering one or more of the following terms: C(2,−2), C(2,2),C(4,−2), C(4,2), C(6,−2), and/or C(6,2).

(G109) The multifocal lens of one or more of the above G examples,wherein the RIQ is characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity functionCSF (F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1),where f specifies the tested spatial frequency, in the range of F_(min)to F_(max);FT denotes a 2D fast Fourier transform;A (ρ, θ) denotes the pupil amplitude function across pupil diameter;W (ρ, θ) denotes wavefront of the test case measured for i=1 to 20

${W( {\rho,\theta} )} = {\sum\limits_{i = 1}^{k}{a_{i}{Z_{i}( {\rho,\theta} )}}}$

Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(G110) The multifocal lens of one or more of the above G examples,wherein the RIQ is characterised by

${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$

wherein:Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;CSF(x, y) denotes the contrast sensitivity functionCSF (F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1),where f specifies the tested spatial frequency, in the range of F_(min)to F_(max);FT denotes a 2D Fourier transform, for example a 2D fast Fouriertransform;A (ρ, θ) denotes the pupil amplitude function across pupil diameter;W (ρ, θ) denotes wavefront of the test case measured for i=1 to k;wherein k is a positive integer;

${W( {\rho,\theta} )} = {\sum\limits_{i = 1}^{k}{a_{i}{Z_{i}( {\rho,\theta} )}}}$

Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

(G111) The multifocal lens of one or more of the above G examples,wherein the multifocal lens includes an optical axis and an aberrationprofile along the optical axis that provides: a focal distance for aC(2,0) Zernike coefficient term; a peak visual Strehl Ratio (‘firstvisual Strehl Ratio’) within a through focus range, and a visual StrehlRatio that remains at or above a second visual Strehl Ratio over thethrough focus range that includes said focal distance, wherein thevisual Strehl Ratio is measured for a model eye with no, orsubstantially no, aberration and is measured along the optical axis forat least one pupil diameter in the range 3 mm to 5 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive, at a wavelengthselected from within the range 540 nm to 590 nm inclusive, and whereinthe first visual Strehl Ratio is at least 0.35, the second visual StrehlRatio is at least 0.1 and the through focus range is at least 1.8Dioptres.

(G112) The multifocal lens of one or more of the above G examples,wherein the multifocal lens includes an optical axis and an aberrationprofile along the optical axis that provides: a focal distance for aC(2,0) Zernike coefficient term; a peak visual Strehl Ratio (‘firstvisual Strehl Ratio’) within a through focus range, and a visual StrehlRatio that remains at or above a second visual Strehl Ratio over thethrough focus range that includes said focal distance, wherein thevisual Strehl Ratio is measured for a model eye with no aberration andis measured along the optical axis for at least one pupil diameter inthe range 3 mm to 5 mm, over a spatial frequency range of 0 to 30cycles/degree inclusive, at a wavelength selected from within the range540 nm to 590 nm inclusive, and wherein the first visual Strehl Ratio isat least 0.35, the second visual Strehl Ratio is at least 0.1 and thethrough focus range is at least 1.8 Dioptres.

(G113) The multifocal lens of one or more of the above G examples,wherein the first visual Strehl Ratio is at least 0.3, 0.35, 0.4, 0.5,0.6, 0.7 or 0.8.

(G114) The multifocal lens of one or more of the above G examples,wherein the second visual

Strehl Ratio is at least 0.1, 0.12, 0.15, 0.18 or 0.2.

(G115) The multifocal lens of one or more of the above G examples,wherein the through focus range is at least 1.7, 1.8, 1.9, 2, 2.1, 2.25or 2.5 Dioptres.

(G116) The multifocal lens of one or more of the above G examples,wherein the lens has a prescription focal distance located within 0.75,0.5, 0.3, or 0.25 Dioptres, inclusive, of an end of the through focusrange.

(G117) The multifocal lens of one or more of the above G examples,wherein the end of the through focus range is the negative power end.

(G118) The multifocal lens of one or more of the above G examples,wherein the end of the through focus range is the positive power end.

(G119) The multifocal lens of one or more of the above G examples,wherein the visual Strehl Ratio remains at or above the second visualStrehl Ratio over the through focus range and over a range of pupildiameters of at least 1 mm, 1.5 mm, 2 mm, 2.5 mm, or 3 mm.

(G120) The multifocal lens of one or more of the above G examples,wherein the combination of higher order aberrations includes at leastone of primary spherical aberration and secondary spherical aberration.

(G121) The multifocal lens of one or more of the above G examples,wherein the higher order aberrations include at least two, three, orfive spherical aberration terms selected from the group C(4,0) toC(20,0).

(G122) The multifocal lens of one or more of the above G examples,wherein the aberration profile can be substantially characterised usingspherical aberration Zernike coefficients C (4, 0) to C (20, 0).

(G123) The multifocal lens of one or more of the above G examples,wherein the RIQ for a substantial portion of the angles over ahorizontal field of at least −10° to +10°, −20° to +20° or −30° to +30°is at least 0.4.

(G124) The multifocal lens of one or more of the above G examples,wherein the RIQ for a substantial portion of the angles over ahorizontal field of at least −10° to +10°, −20° to +20° or −30° to +30°is at least 0.35.

(G125) The multifocal lens of one or more of the above G examples,wherein the RIQ for a substantial portion of the angles over ahorizontal field of at least −10° to +10°, −20° to +20° or −30° to +30°is at least 0.3.

(G126) The multifocal lens of one or more of the above G examples,wherein the lens is one or more of the following: contact lens, cornealonlays, corneal inlays, anterior chamber intraocular lens or posteriorchamber intraocular lens.

(G127) The multifocal lens of one or more of the above G examples,wherein the lens is one of the following: contact lens, corneal onlays,corneal inlays, anterior chamber intraocular lens or posterior chamberintraocular lens.

(G128) The multifocal lens of one or more of the above G examples,wherein a first multifocal lens is provided based on one or more of theabove of the G examples and a second multifocal lens is provided basedon one or more of the above of the G examples to form a pair of lenses.

(G129) The multifocal lens of one or more of the above G examples,wherein the first multifocal lens is provided based on one or more ofthe above of the G examples and a second lens is provided to form a pairof lenses.

(G130) The multifocal lens of one or more of the above G examples,wherein a pair of multifocal lenses are provided for use by anindividual to substantially correct the individual's vision.

(G131) The lens of one or more of the above G examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(G132) The lens of one or more of the above G examples, wherein theamount of light passing through the lens is at least 80%, 85%, 90%, 95%or 99%.

(G133) A method for making or using one or more of the multifocal lensesof one or more of the above G examples.

Example Set H

(H1) A system of lenses comprising: a series of lenses, wherein thelenses in the series of lenses have the following properties: at leasttwo spherical aberration terms selected at least in part from a groupcomprising spherical aberration coefficients from C(4,0) to C(20,0),that provides correction of astigmatism up to 1 Dioptre withoutsubstantial use of rotationally stable toric lens design features; andwherein the lenses in the series of lenses eliminate the need formaintaining additional inventory for astigmatic corrections relating tocylinder powers of 0.5, 0.75 and 1D, resulting in a reduction of stockkeeping units by at least six, eight, twelve, sixteen, eighteen, thirtysix, fifty-four or 108 times for each sphere power.

Example Set J

(J1) A multifocal lens for an eye comprising: at least one optical axis;at least one wavefront aberration profile associated with the opticalaxis and the prescription focal power of the lens; wherein, themultifocal lens is configured to expand the depth-of-focus of the eye byaltering the retinal image quality over a range of distances viamanipulation of the at least one wavefront aberration profile for theeye.

(J2) A multifocal lens for an eye comprising: at least one optical axis;at least one wavefront aberration profile associated with the opticalaxis and the aberration profile is comprised of at least two sphericalaberration terms and the prescription focal power of the lens; whereinthe lens is configured such that the lens expands the depth-of-focus ofthe eye by altering the retinal image quality over a range of distancesvia manipulation of at least one wavefront aberration profile for theeye.

(J3) A multifocal lens for an eye comprising: at least one optical axis;at least one wavefront aberration profile associated with the opticalaxis, and the aberration profile is comprised of: at least two sphericalaberration selected at least in part from a group comprising Zernikecoefficients C(4,0) to C(20,0), and a prescription focal power of thelens that may be provided at least in part by C(2,0) Zernike coefficientterm either with, or without, one or more prescription offset terms;wherein, the multifocal lens is configured to expand the depth-of-focusof the eye by improving the retinal image quality over a range ofdistances via manipulation of the at least one wavefront aberrationprofile.

(J4) The lens of one or more of the above J examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(J5) The lens of one or more of the above J examples, wherein the amountof light passing through the lens is at least 80%, 85%, 90%, 95% or 99%.

Example Set K

(K1) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile ischaracterised upon testing by a function that is non-monotonic over asubstantial portion of the half-chord optical zone of the lens.

(K2) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile ischaracterised by a function that is non-monotonic over a substantialportion of the half-chord optical zone of the lens.

(K3) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile ischaracterised by a function that is aperiodic over a substantial portionof the half-chord optical zone of the lens.

(K4) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile ischaracterised upon testing by a function that is aperiodic over asubstantial portion of the half-chord optical zone of the lens.

(K5) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile ischaracterised by a function that is aperiodic and non-monotonic over asubstantial portion of the half-chord optical zone of the lens.

(K6) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile ischaracterised upon testing by a function that is aperiodic andnon-monotonic over a substantial portion of the half-chord optical zoneof the lens.

(K7) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile is configuredsuch that the power profile is non-monotonic over a substantial portionof the half-chord optical zone of the lens.

(K8) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile is configuredsuch that the power profile is aperiodic over a substantial portion ofthe half-chord optical zone of the lens.

(K9) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile, the power profile is configuredsuch that the power profile is aperiodic and non-monotonic over asubstantial portion of the half-chord optical zone of the lens.

(K10) A lens comprising: an optical axis; at least two surfaces; andwherein the lens has at least one power profile, the power profile isconfigured such that the absolute of a first derivative of the powerprofile has at least 5 peaks whose absolute amplitude is greater than0.025 with units of 1D per 0.01 mm along its half-chord.

(K11) A lens comprising: an optical axis; at least two surfaces; andwherein the lens has at least one power profile, the power profile ischaracterised such that the absolute of a first derivative of the powerprofile has at least 5 peaks whose absolute amplitude is greater than0.025 with units of 1D per 0.01 mm along its half-chord.

(K12) The multifocal lens comprising: an optical axis; at least twosurfaces; and wherein the multifocal lens has a power profile such thatan absolute of a first derivative of the power profile, as a function ofhalf-chord diameter, has at least 5 peaks whose absolute amplitude isgreater than 0.025 with units of 1D per 0.01 mm along its half-chorddiameter.

(K13) The lens of one or more of the above of K examples, wherein thelens is configured at least in part on an aberration profile associatedwith the optical axis.

(K14) The lens of one or more of the above of K examples, wherein thelens has an aberration profile comprised of a defocus term and at leasttwo spherical aberration terms.

(K15) The lens of one or more of the above of K examples, wherein thelens is a multifocal or bifocal. K15 The lens of one or more of theabove of K examples, wherein the substantial portion of the half-chordis 50%, 60%, 70%, 80%, 90% or 95% of the half-chord.

(K16) A method of characterising lens power profile comprising the stepsof: measuring the spatially resolved power profile; computing a firstderivative of the power profile; and analysing or describing the powerprofile as a first derivative of the power profile.

(K17) The method of one or more of the above of K examples, wherein thefirst of derivative of the power profile is an absolute of the firstderivative of the power profile.

(K18) A method of characterising lens power profile comprising the stepsof: measuring the power profile; computing a Fourier transform of thepower profile; and describing the power profile as a Fourier spectrum,wherein a normalised absolute amplitude of the Fourier transform of thepower profile is greater than 0.2 at one or more spatial frequencies ator above 1.25 cycles per millimetre.

(K19) The method of one more K examples, wherein the Fourier spectrum ofthe power profile is the amplitude of the Fourier spectrum.

(K20) The method of one more K examples, wherein the Fourier spectrum ofthe power profile is the phase of the Fourier spectrum.

(K21) The method of one more K examples, wherein the Fourier spectrum isan absolute of the Fourier spectrum.

(K22) The method of one more K examples, wherein the Fourier spectrum isa real of the Fourier spectrum.

(K23) The method of one more K examples, wherein the Fourier spectrum isa normalised absolute of the Fourier spectrum.

(K24) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has at least one power profile that is characterised by anormalised absolute amplitude of the Fourier transform of the powerprofile that is greater than 0.2 at one or more spatial frequencies ator above 1.25 cycles per millimetre.

(K25) The lens of one or more of the above K examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(K26) The lens of one or more of the above K examples, wherein theamount of light passing through the lens is at least 80%, 85%, 90%, 95%or 99%.

Example Set L

(L1) A multifocal lens comprising: an optical axis; an effective nearaddition power of at least 1D; an optic zone associated with the opticalaxis with an aberration profile; wherein the aberration profile iscomprised of at least two spherical aberration terms; and the multifocallens is configured to provide minimal ghosting along a range of visualdistances, including near, intermediate and far distances.

(L2) The multifocal lens of one or more of the above L examples, whereinminimal ghosting is an average rating of two or less for a group of atleast 15 subjects on a 1 to 10 visual analogue scale.

(L3) The multifocal lens of one or more of the above L examples, whereinminimal ghosting is an average rating of two or less for a group of atleast 15 subjects on a 1 to 10 visual analogue scale, wherein the atleast 15 subjects are selected from a representative population ofindividuals with one or more of the following conditions: myopia,hyperopia, astigmatism and presbyopia.

(L4) The multifocal lens of one or more of the above L examples, whereinminimal ghosting is an average rating of two or less for a group of atleast 15 subjects on a 1 to 10 visual analogue scale, wherein the atleast 15 subjects are selected from a representative population ofemmetropic non-presbyopes.

(L5) The multifocal lens of one or more of the above L examples, whereinminimal ghosting is a score of less than or equal to 2.4, 2.2, 2, 1.8,1.6 or 1.4 on the vision analogue rating scale 1 to 10 units utilisingthe average visual performance of the lens in use on a sample of peopleneeding vision correction and/or therapy, for one or more of thefollowing: myopia, hyperopia, astigmatism, emmetropia and presbyopia.

(L6) The multifocal lens of one or more of the above L examples, whereinat least 30% of the individuals tested report no ghosting at near visualdistances and far visual distances.

(L7) The multifocal lens of one or more of the above L examples, whereinat least 30% of the individuals tested report no ghosting for visualdistances along a range of substantially continuous visual distances,including near, intermediate and far distances.

(L8) The multifocal lens of one or more of the above L examples, whereinat least 40% of the individuals tested report no ghosting at near visualdistances and far visual distances.

(L9) The multifocal lens of one or more of the above L examples, whereinat least 40% of the individuals tested report no ghosting at near,intermediate and far distances.

(L10) The multifocal lens of one or more of the above L examples,wherein at least 40% of the individuals tested report a rating of lessthan two for ghosting at both near and far visual distances reported.

(L11) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens include an aberration profileassociated with the optical axis; the aberration profile is comprised ofa defocus term and at least two spherical aberration terms; and aneffective additional power of at least 1D; the multifocal lens isconfigured to provide: an average rating of at least 9 for distancevision on a visual analogue scale of 1 to 10; an average rating of atleast 8.5 for intermediate vision on the visual analogue scale; anaverage rating of at least 7.5 for near vision on the visual analoguescale; an average rating of less than 2 for ghosting for far vision onthe visual analogue scale; an average rating of less than 2 for ghostingfor near vision on the visual analogue scale; and when tested on asample of at least 15 participants who are correctable to at least 6/6or better in both eyes and have an astigmatism of less than 1.5D and whoare selected from an affected population.

(L12) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens include an aberration profileassociated with the optical axis; the aberration profile is comprised ofa defocus term and at least two spherical aberration terms; and aneffective additional power of at least 1D; the multifocal lens isconfigured to provide: at least 60% of the individuals tested for farvisual distances report a score of greater than 9 on a visual analoguescale ranging between 1 and 10; at least 50% of the individuals testedfor intermediate visual distances report a score of greater than 9 onthe visual analogue scale; at least 30% of the individuals tested fornear visual distances report a score of greater than 9 on the visualanalogue scale; below 15% of the individuals tested for ghosting atdistance report a score of less than 3 on the visual analogue scale; atleast 40% of the individuals tested for ghosting at either distance ornear report a score of less than 2 on the visual analogue scale; and atleast 25% of the individuals tested report a score of greater than 9 onthe visual analogue scale for cumulative vision encompassing distance,intermediate, near, lack of ghosting at distance, and lack of ghostingat near.

(L13) The multifocal lens of one or more of the above L examples,wherein at least 30% of the individuals tested report a score of greaterthan 9 on the visual analogue scale for cumulative vision encompassingdistance, intermediate, near, lack of ghosting at distance, and lack ofghosting at near.

(L14) The multifocal lens of one or more of the above L examples,wherein at least 35% of the individuals tested report a score of greaterthan 9 on the visual analogue scale for cumulative vision encompassingdistance, intermediate, near, lack of ghosting at distance, and lack ofghosting at near.

(L15) The multifocal lens of one or more of the above L examples,wherein at least 40% of the individuals tested report a score of greaterthan 9 on the visual analogue scale for cumulative vision encompassingdistance, intermediate, near, lack of ghosting at distance, and lack ofghosting at near.

(L16) The multifocal lens of one or more of the above L examples,wherein at least 55% of the individuals tested for intermediate visualdistances report a score of greater than 9 on a visual analogue scaleranging between 1 and 10.

(L17) The multifocal lens of one or more of the above L examples,wherein at least 35% of the individuals tested for near visual distancesreport a score of greater than 9 on the visual analogue scale rangingbetween 1 and 10.

(L18) The multifocal lens of one or more of the above L examples,wherein at least 40% of the individuals tested for near visual distancesreport a score of greater than 9 on the visual analogue scale rangingbetween 1 and 10.

(L19) The multifocal lens of one or more of the above L examples,wherein at least 45% of the individuals tested for near visual distancesreport a score of greater than 9 on the visual analogue scale rangingbetween 1 and 10.

(L20) The multifocal lens of one or more of the above L examples,wherein at least 30% of the individuals tested report a score of greaterthan 9 on the visual analogue scale for cumulative vision encompassingdistance, intermediate, near, lack of ghosting at distance, and lack ofghosting at near.

(L21) The multifocal lens of one or more of the above L examples,wherein at least 30% of the individuals tested report a score of greaterthan 9 on the visual analogue scale for cumulative vision encompassingdistance, intermediate, near, lack of ghosting at distance, and lack ofghosting at near.

(L22) The multifocal lens of one or more of the above L examples,wherein at least 35% of the individuals tested report a score of greaterthan 9 on the visual analogue scale for cumulative vision encompassingdistance, intermediate, near, lack of ghosting at distance, and lack ofghosting at near.

(L23) The multifocal lens of one or more of the above L examples,wherein at least 40% of the individuals tested report a score of greaterthan 9 on the visual analogue scale for cumulative vision encompassingdistance, intermediate, near, lack of ghosting at distance, and lack ofghosting at near.

(L24) The multifocal lens of one or more of the above L examples,wherein at least 45% of the individuals tested report a score of greaterthan 9 on the visual analogue scale for cumulative vision encompassingdistance, intermediate, near, lack of ghosting at distance, and lack ofghosting at near.

(L25) The multifocal lens of one or more of the above L examples,wherein at least 45% of the individuals tested for ghosting at eitherdistance or near report a score of less than 2 on the visual analoguescale.

(L26) The multifocal lens of one or more of the above L examples,wherein at least 50% of the individuals tested for ghosting at eitherdistance or near report a score of less than 2 on the visual analoguescale.

(L27) The multifocal lens of one or more of the above L examples,wherein at least 55% of the individuals tested for ghosting at eitherdistance or near report a score of less than 2 on the visual analoguescale.

(L28) The multifocal lens of one or more of the above L examples,wherein at least 60% of the individuals tested for ghosting at eitherdistance or near report a score of less than 2 on the visual analoguescale.

(L29) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens include an aberration profileassociated with the optical axis; the aberration profile is comprised ofa defocus term and at least two spherical aberration terms; and aneffective additional power of at least 1D; the multifocal lens isconfigured to provide: an average visual acuity for far visual distancesof at least 0.00 on a LogMAR visual acuity chart; an average visualacuity for intermediate visual distances at least 0.00 on a LogMARvisual acuity chart; an average visual acuity for near visual distancesat least 0.02 on a LogMAR visual acuity chart; an average rating of lessthan 2 for ghosting for far vision on the visual analogue scale; anaverage rating of less than 2 for ghosting for near vision on the visualanalogue scale; and when tested on a sample of at least 15 participantswho are correctable to at least 6/6 visual acuity or better in both eyesand have an astigmatism of less than 1.5D.

(L30) The multifocal lens of one or more of the above L examples,wherein the multifocal lens has an effective additional power of atleast 1.25D.

(L31) The multifocal lens of one or more of the above L examples,wherein the multifocal lens has an effective additional power of atleast 1.5D.

(L32) The lens of one or more of the above L examples, wherein the lensdoes not substantially reduce the amount of light passing through thelens.

(L33) The lens of one or more of the above L examples, wherein theamount of light passing through the lens is at least 80%, 85%, 90%, 95%or 99%.

(L34) The multifocal lens of one or more of the above L examples,wherein the participants are selected from an affected population.

(L35) A multifocal lens comprising: an optical axis; the opticalproperties of the multifocal lens are configured or described based onan aberration profile associated with the optical axis; the aberrationprofile is comprised of a defocus term and at least two sphericalaberration terms; and the multifocal lens is configured to provide: anaverage subjective visual rating of at least 9 for distance vision on avisual analogue scale; an average subjective visual rating of at least 9for intermediate vision on a visual analogue scale; an averagesubjective visual rating of at least 7.5 for near vision on a visualanalogue scale; an average subjective visual rating of less than 2 forfar vision on a ghosting analogue scale; and/or an average subjectivevisual rating of less than 2 for near vision on a ghosting analoguescale; when tested on a sample of at least 15 participants randomlyselected from an affected population.

(L36) It will be understood that the inventions disclosed and defined inthis specification extends to alternative combinations of two or more ofthe individual features mentioned or evident from the text or drawings.These different combinations constitute various alternative aspects ofthe embodiments disclosed.

Example Set M

(M1) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has a power profile, the power profile has a best fit with aR²>0.975 and/or a RMSE<0.15 D when characterised upon testing by afunction that uses between 40 and 80 non-zero, symmetric, Zernike powerpolynomial coefficients.

(M2) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has a power profile, the power profile has a best fit with aR²>0.975 and/or a RMSE<0.15 D when characterised upon testing by afunction that uses at least 14 non-zero coefficients of a Fourier seriesexpansion.

(M3) A lens comprising: an optical axis; at least two surfaces; whereinthe lens has a power profile, the power profile has a best fit with aR²>0.975 and/or a RMSE<0.15 D when characterised upon testing by afunction that uses at least 14 non-zero, coefficients of a Fourierseries and between 40 and 80 non-zero, symmetric, Zernike powerpolynomial coefficients.

(M4) The lens of one or more of the M examples, wherein the lens furthercomprises a focal distance and an aberration profile with three or morehigher order aberrations; wherein the aberration profile provides for amodel eye with no aberrations, or substantially no aberrations, and anon-axis length equal to, or substantial equal to, the focal distance: aretinal image quality (RIQ) with a through focus slope that degrades ina direction of eye growth; and a RIQ of at least 0.3; wherein the RIQ isvisual Strehl Ratio measured substantially along the optical axis for atleast one pupil diameter in the range 3 mm to 6 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive and at a wavelengthselected from within the range 540 nm to 590 nm inclusive.

(M5) The lens of one or more of the above M examples, wherein the lensfurther comprises a focal distance and an aberration profile with threeor more higher order aberrations; wherein the aberration profileprovides for a model eye with substantially no aberrations an on-axislength equal to, or substantially equal to, the desired focal distance;a retinal image quality (RIQ) with a through focus slope that improvesin a direction of eye growth; and a RIQ of at least 0.3; wherein the RIQis measured substantially along the optical axis for at least one pupildiameter in the range 3 mm to 6 mm, over a spatial frequency range of 0to 30 cycles/degree inclusive and at a wavelength selected from withinthe range 540 nm to 590 nm inclusive.

(M6) The lens of one or more of the above M examples, wherein the lensfurther comprises an aberration profile with three or more higher orderaberrations; wherein the aberration profile provides: a focal distancefor a C(2,0) Zernike coefficient term; a first visual Strehl Ratiowithin a through focus range, and the first visual Strehl Ratio thatremains at or above a second visual Strehl Ratio over the through focusrange that includes said focal distance, wherein the first and secondvisual Strehl Ratio is measured for a model eye with no, orsubstantially no, aberration and is measured along the optical axis forat least one pupil diameter in the range 3 mm to 5 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive, at a wavelengthselected from within the range 540 nm to 590 nm inclusive, and whereinthe first visual Strehl Ratio is at least 0.35, the second visual StrehlRatio is at least 0.1 and the through focus range is at least 1.8Dioptres

(M7) The lens of one or more of the above M examples, wherein theaberration profile comprises at least four spherical aberration termsselected from the group C(4,0) to C(20,0).

(M8) The lens of one or more of the above M examples, wherein theaberration profile comprises at least five spherical aberration termsselected from the group C(4,0) to C(20,0).

(M9) The lens of one or more of the above M examples, wherein theaberration profile comprises at least six spherical aberration termsselected from the group C(4,0) to C(20,0).

(M10) The lens of one or more of the above M examples, wherein theaberration profile comprises at least seven spherical aberration termsselected from the group C(4,0) to C(20,0).

(M11) The lens of one or more of the above M examples, wherein theaberration profile provides an effective near additional power of atleast 1 D; and wherein the lens is configured to provide a visualperformance over near, intermediate and far distances that is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance; and whereinthe lens is configured to provide minimal ghosting at far, intermediateand near distances.

(M12) The lens of one or more of the above M examples, wherein thefitted coefficients are substantially non-zero.

Example Set P

(P1) An intra-ocular lens system for an eye comprising: a first lenscomprising: a first optical axis; the optical properties of the firstlens are at least in part configured with a first aberration profile;the first aberration profile is comprised of a first defocus term; asecond lens comprising: a second optical axis; the optical properties ofthe second lens are at least in part configured with a second aberrationprofile; the second aberration profile is comprised of a second defocusterm; wherein at least one of the first lens or the second lens furthercomprise at least three higher order aberration terms.

(P2) The intra-ocular lens system of one or more of the above Pexamples, wherein the first lens and the second lens are adjacent toeach other.

(P3) The intra-ocular lens system of one or more of the above Pexamples, wherein the first lens comprises at least three higher orderaberration terms and the second lens comprises at least three higherorder aberration terms.

(P4) The intra-ocular lens system of one or more of the above Pexamples, wherein the intra-ocular lens provides a visual performanceover one or more of the following: near, intermediate and far distances,and the visual performance is at least substantially equivalent to thevisual performance of a correctly prescribed single-vision intra-ocularlens at the far visual distance; and is configured to provide minimalghosting at far, intermediate and near distances.

(P5) The intra-ocular lens system of one or more of the above Pexamples, wherein at least one of the first lens or the second lenscomprises at least four higher order aberration terms.

(P6) The intra-ocular lens system of one or more of the above Pexamples, wherein at least one of the first lens or the second lenscomprises at least five higher order aberration terms.

(P7) The intra-ocular lens system of one or more of the above Pexamples, wherein at least one of the first lens or the second lenscomprises at least six higher order aberration terms.

(P8) The intra-ocular lens system of one or more of the above Pexamples, wherein at least one of the first lens or the second lenscomprises at least seven higher order aberration terms.

(P9) The intra-ocular lens system of one or more of the above Pexamples, wherein the first lens comprise at least four higher orderaberration terms and the second lens comprise at least four higher orderaberration terms.

(P10) The intra-ocular lens system of one or more of the above Pexamples, wherein the first lens comprise at least five higher orderaberration terms and the second lens comprise at least five higher orderaberration terms.

(P11) The intra-ocular lens system of one or more of the above Pexamples, wherein the first lens comprise at least six higher orderaberration terms and the second lens comprise at least six higher orderaberration terms.

(P12) The intra-ocular lens system of one or more of the above Pexamples, wherein the first lens comprise at least seven higher orderaberration terms and the second lens comprise at least seven higherorder aberration terms.

(P13) The intra-ocular lens system of one or more of the above Pexamples, wherein the one or more of the higher order aberration termsare spherical aberration terms.

(P14) The intra-ocular lens system of one or more of the above Pexamples, wherein the higher order aberration terms are sphericalaberration terms.

(P15) The intra-ocular lens system of one or more of the above Pexamples, wherein the at least three spherical aberration terms areselected from the group C (4, 0) to C (20, 0).

(P16) The intra-ocular lens system of one or more of the above Pexamples, wherein the at least four spherical aberration terms areselected from the group C (4, 0) to C (20, 0).

(P17) The intra-ocular lens system of one or more of the above Pexamples, wherein the at least five spherical aberration terms areselected from the group C (4, 0) to C (20, 0).

(P18) The intra-ocular lens system of one or more of the above Pexamples, wherein the at least six spherical aberration terms areselected from the group C (4, 0) to C (20, 0).

(P19) The intra-ocular lens system of one or more of the above Pexamples, wherein the at least seven spherical aberration terms selectedfrom the group C (4, 0) to C (20, 0).

(P20) The intra-ocular lens system of one or more of the above Pexamples, wherein the intra-ocular system with the at least three higheraberration profile provides: a focal distance; a first visual StrehlRatio within a through focus range, and the first visual Strehl Ratiothat remains at or above a second visual Strehl Ratio over the throughfocus range that includes said focal distance, wherein the visual StrehlRatio is measured for a model eye with no, or substantially no,aberration and is measured along the optical axis for at least one pupildiameter in the range 3 mm to 5 mm, over a spatial frequency range of 0to 30 cycles/degree inclusive, at a wavelength selected from within therange 540 nm to 590 nm inclusive, and wherein the first visual StrehlRatio is at least 0.3, the second visual Strehl Ratio is at least 0.1and the through focus range is at least 1.8 Dioptres.

(P21) The intra-ocular lens system of one or more of the above Pexamples, wherein the intra-ocular system with the at least three higheraberrations provide: a focal distance; a first Strehl Ratio within athrough focus range, and the first Strehl Ratio that remains at or abovea second Strehl Ratio over the through focus range that includes saidfocal distance, wherein the Strehl Ratio is measured along the opticalaxis for at least one portion of the optic zone diameter in the range 3mm to 5 mm, over a spatial frequency range of 0 to 30 cycles/degreeinclusive, at a wavelength selected from within the range 540 nm to 590nm inclusive, and wherein the first Strehl Ratio is at least 0.2, thesecond Strehl Ratio is at least 0.1 and the through focus range is atleast 1.8 Dioptres.

(P22) The intra-ocular lens system of one or more of the above Pexamples, wherein the first visual Strehl Ratio is at least 0.28, 0.25,0.22 or 0.20.

(P23) The intra-ocular lens system of one or more of the above Pexamples, wherein the second visual Strehl Ratio is at least 0.08, 0.1,0.12, 0.14, 0.16, 0.18 or 0.2.

(P24) The intra-ocular lens system of one or more of the above Pexamples, wherein the through focus range is at least 2 Dioptres, 2.2Dioptres or 2.5 Dioptres.

(P25) The intra-ocular lens system of one or more of the above Pexamples, wherein the end of the through focus range is the negativepower end.

(P26) The intra-ocular lens system of one or more of the above Pexamples, wherein the end of the through focus range is the positivepower end.

(P27) The intra-ocular lens system of one or more of the above Pexamples, wherein the first visual Strehl Ratio remains at or above thesecond visual Strehl Ratio over the through focus range and over a rangeof pupil diameters of at least 1 mm, 1.5 mm or 2 mm.

(P28) The intra-ocular lens system of one or more of the above Pexamples, wherein the first Strehl Ratio remains at or above the secondStrehl Ratio over the through focus range and over a portion of opticzone diameters of at least 1 mm, 1.5 mm or 2 mm.

(P29) The intra-ocular lens system of one or more of the above Pexamples; wherein the intra-ocular lens system is configured to providea visual performance on a presbyopic eye substantially equivalent to thevisual performance of a single-vision lens on the pre-presbyopic eye;and wherein the first and the second lens have an aperture size greaterthan 1.5 mm.

(P30) The intra-ocular lens system of one or more of the above Pexamples; wherein the intra-ocular lens system is configured to providea visual performance, along a range of substantially continuous visualdistances, including near, intermediate and far distances.

(P31) The intra-ocular lens system of one or more of the above Pexamples; wherein the intra-ocular lens system is configured to provideminimal ghosting at far, intermediate and near distances.

(P32) The intra-ocular lens system of one or more of the above Pexamples; wherein the intra-ocular lens system is configured to providenear visual acuity of at least 6/6 in individuals that can achieve 6/6visual acuity.

(P33) The intra-ocular lens system of one or more of the above Pexamples; wherein the intra-ocular lens system is configured to provideat least acceptable visual performance at near distances.

(P34) The intra-ocular lens system of one or more of the above Pexamples; wherein the intra-ocular lens system is configured to providea visual performance, along a range of substantially continuous nearvisual distances, wherein the visual performance of the intra-ocularlens system is at least substantially equivalent to the visualperformance of a correctly prescribed single-vision lens at the farvisual distance.

(P35) The intra-ocular lens system of one or more of the above Pexamples; wherein the intra-ocular lens system is configured to providea visual performance, along a range of substantially continuous visualdistances, including near, intermediate and far distances, wherein thevisual performance of the intra-ocular lens system is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance.

Example Set Q

(Q1) A multifocal lens comprising: an optical axis; at least twosurfaces; wherein the lens has at least one power profile and the powerprofile has at least three peaks and/or three troughs along thehalf-chord diameter of the optic zone of the multifocal lens.

(Q2) The multifocal lens of the example Q1, wherein the at least threepeaks and/or three troughs are further characterised by having anamplitude between one of the peaks and an adjacent trough that is atleast 0.5 D, 1 D, 2 D or 3 D.

(Q3) The multifocal lens of the example Q1, wherein the at least threepeaks and/or three troughs are further characterised by having anamplitude between one of the peaks and an adjacent trough that is atleast 0.25 D, 0.5 D, 0.75 D, 1 D, 1.25 D, 1.5 D, 1.75 D, 2 D, 2.25, 2.5D, 2.75 D, 3 D, 3.25 D, 3.5D, 3.75 D or 4 D.

(Q4) The multifocal lens of the example Q1, wherein the at least threepeaks and/or three troughs are further characterised by having anamplitude between one of the peaks and an adjacent trough that isbetween 0.5 D and 1 D, 1.25 D and 2 D, 2.25, and 3 D or 3.25 D and 4 D.

(Q5) The multifocal lens of one or more of the above Q examples, whereinthe power profile starts substantially in the vicinity of a trough or apeak.

(Q6) The multifocal lens of one or more of the above Q examples, whereinthe spatial separation between each peak and its and adjacent troughs ofthe power profile of the multifocal lens is at least 0.125 mm, 0.25 mm,0.5 mm, 0.75 mm or 1 mm.

(Q7) The multifocal lens of one or more of the above Q examples, whereinthe difference between the amplitudes of two adjacent peaks or twoadjacent troughs of the power profile of the multifocal lens is between0.5 D and 1 D, 1.25 D and 2 D, 2.25, and 3 D or 3.25 D and 4 D.

(Q8) The multifocal lens of one or more of the above Q examples, whereinthe difference between the amplitudes of two adjacent peaks or twoadjacent troughs of the power profile of the multifocal lens is at least0.5 D, 1 D, 2 D or 3 D.

(Q9) The multifocal lens of one or more of the above Q examples, whereinthe difference between the amplitudes of two adjacent peaks or twoadjacent troughs of the power profile of the multifocal lens is at least0.25D, 0.5 D, 0.75 D, 1 D, 1.25 D, 1.5 D, 1.75 D, 2 D, 2.25, 2.5 D, 2.75D, 3 D, 3.25 D, 3.5D, 3.75 D or 4 D.

(Q10) The multifocal lens of one or more of the above Q examples,wherein the peaks and troughs of the power profile of the multifocallens are generated by surface modulations of the front surface of themultifocal lens.

(Q11) The multifocal lens of one or more of the above Q examples,wherein the peaks and troughs of the power profile of the multifocallens are generated by surface modulations of the back surface of themultifocal lens.

(Q12) The multifocal lens of one or more of the above Q examples,wherein the peaks and troughs of the power profile of the multifocallens are generated by surface modulations of the front and the backsurface of the multifocal lens.

(Q13) The multifocal lens of one or more of the above Q examples,wherein the spatial separation between each peak and its and adjacenttroughs of the power profile of the multifocal lens is at least 0.125mm, 0.25 mm, 0.5 mm, 0.75 mm or 1 mm.

Example Set R

(R1) An ophthalmic lens, the lens having an optic zone, an optical axisand an aberration profile associated with the optical axis, theaberration profile having a focal power and three or more higher orderaberrations, wherein the aberration profile produces a Strehl ratio witha through focus slope that degrades in the negative power end and theStrehl ratio is at least 0.2 at the focal distance; and wherein theStrehl Ratio is measured substantially along the optical axis, for atleast a portion of the optic zone diameter ranging from 3 mm to 6 mm,over a spatial frequency range of 0 to 30 cycles/degree inclusive and ata wavelength selected from within the range 540 nm to 590 nm inclusive.

(R2) An ophthalmic lens, the lens having an optic zone, an optical axisand an aberration profile associated with the optical axis, theaberration profile having a focal power and three or more higher orderaberrations, wherein the aberration profile produces a Strehl ratio witha through focus slope that improves in the negative power end and theStrehl ratio is at least 0.2 at the focal distance; and wherein theStrehl Ratio is measured substantially along the optical axis, for atleast a portion of the optic zone diameter ranging from 3 mm to 6 mm,over a spatial frequency range of 0 to 30 cycles/degree inclusive and ata wavelength selected from within the range 540 nm to 590 nm inclusive.

(R3) An ophthalmic lens, the lens having an optic zone, an optical axisand an aberration profile associated with the optical axis, theaberration profile having a focal distance and three or more higherorder aberrations; wherein the aberration profile provides: a firstStrehl Ratio within a through focus range, and the first Strehl Ratioremains at or above a second Strehl Ratio over the through focus rangethat includes said focal distance, wherein the first and the secondStrehl Ratio are calculated for at least a portion of the optic zonediameter in the range 3 mm to 5 mm, over a spatial frequency range of 0to 30 cycles/degree inclusive, at a wavelength selected from within therange 540 nm to 590 nm inclusive, and wherein the first Strehl Ratio isat least 0.20, the second Strehl Ratio is at least 0.1 and the throughfocus range is at least 1.8 D.

(R4) The ophthalmic lens of the example R1, wherein the lens isconfigured to be used with a myopic eye.

(R5) The ophthalmic lens of the example R2, wherein the lens isconfigured to be used with a hyperopic eye.

(R6) The ophthalmic lens of one or more R examples, wherein the Strehlratio at the focal distance is at least 0.22, 0.24, 0.26 or 0.28.

(R7) The ophthalmic lens of one or more R examples, wherein the firstStrehl ratio is at least 0.22, 0.24, 0.26 or 0.28.

(R8) The ophthalmic lens of one or more R examples, wherein the secondStrehl ratio is at least 0.08, 0.1, 0.12 or 0.14.

(R9) The ophthalmic lens of one or more R examples, wherein thethrough-focus range is at least 2 D, 2.2 D or 2.4 D.

(R10) The ophthalmic lens of one or more R examples, wherein the higherorder aberrations comprises at least four spherical aberration termsselected from the group C(4,0) to C(20,0).

(R11) The ophthalmic lens of one or more R examples, wherein the higherorder aberrations comprises at least five spherical aberration termsselected from the group C(4,0) to C(20,0).

(R12) The ophthalmic lens of one or more R examples, wherein the higherorder aberrations comprises at least six spherical aberration termsselected from the group C(4,0) to C(20,0).

(R13) The ophthalmic lens of one or more R examples, wherein the higherorder aberrations comprises at least seven spherical aberration termsselected from the group C(4,0) to C(20,0).

(R14) The lens of one or more of the above R examples, wherein theaberration profile provides an effective near additional power of atleast 1 D; wherein the lens is configured to provide a visualperformance over near, intermediate and far distances that is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance; and whereinthe lens is configured to provide minimal ghosting at far, intermediateand near distances.

(R15) The lens of one or more of the above R examples, wherein theStrehl ratio is characterised by

${R\; I\; Q} = \frac{{\int{\int_{- {Fmin}}^{+ {Fmax}}( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )}}\;}{\int{\int_{- {Fmin}}^{+ {Fmax}}( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )}}$

wherein:f specifies the tested spatial frequency, in the range of F_(min) toF_(max);Fmin is 0 cycles/degree and Fmax is in the range of 5 to 30cycles/degree;FT denotes a 2D Fourier transform, for example a 2D fast Fouriertransform;A (ρ, θ) denotes the pupil amplitude function across pupil diameter;W (ρ, θ) denotes wavefront of the test case measured for i=1 to k;wherein k is a positive integer;

${W( {\rho,\theta} )} = {\sum\limits_{i = 1}^{k}{a_{i}{Z_{i}( {\rho,\theta} )}}}$

Wdiff (ρ, θ) denotes wavefront of the diffraction limited case;ρ and θ are normalised polar coordinates, where ρ represents the radialcoordinate and θ represents the angular coordinate or azimuth; andλ denotes wavelength.

Example Set S

(S1) A lens for an eye, the lens having a first optical axis and anaberration profile associated with the first optical axis, theaberration profile comprising: a focal distance; and higher orderaberrations having at least one primary spherical aberration componentC(4,0) and a secondary spherical aberration component C(6,0), whereinthe aberration profile provides, for a model eye having a second opticalaxis, with no aberrations, or substantially no aberrations, and a lengthalong the second optical axis equal to, or substantial equal to, thefocal distance; and a retinal image quality (RIQ) of at least 0.25wherein the RIQ is a visual Strehl Ratio measured substantially alongthe second optical axis for at least one pupil diameter in the range 3mm to 6 mm.

(S2) The lens of the example S1, wherein the visual Strehl ratio ismeasured within a spatial frequency range from one of the following: 5to 20 cycles/degree, 10 to 20 cycles/degree, 15 to 30 cycles/degree, 20to 35 cycles/degree or 25 to 40 cycles/degree for a range of wavelengthsselected from within the range 380 nm to 800 nm inclusive.

(S3) The lens of the example S2, wherein the range of wavelengths isselected from within the range 540 nm to 590 nm inclusive.

(S4) The lens of example S2, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 5° from the second optical axis, or from on-axis to the secondoptical axis to 10° from the second optical axis.

(S5) The lens of example S2, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 5° from the second optical axis, or from on-axis to the secondoptical axis to 15° from the second optical axis.

(S6) The lens of example S3, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 5° from the second optical axis, or from on-axis to the secondoptical axis to 10° from the second optical axis.

(S7) The lens of example S3, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 5° from the second optical axis, or from on-axis to the secondoptical axis to 15° from the second optical axis.

(S8) The lens of example S2, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 10° from the second optical axis, or from on-axis to the secondoptical axis to 20° from the second optical axis.

(S9) The lens of example S3, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 10° from the second optical axis, or from on-axis to the secondoptical axis to 20° from the second optical axis.

(S10) The lens of examples S1 to S9, wherein the lens is configured toprovide a visual performance for the eye with a second optical axis, atat least one visual distance that is at least equivalent to the visualperformance for the eye of a correctly prescribed single-vision lens atthe visual distance, wherein the visual performance is visual acuity andthe lens has an aperture size greater than 1.5 mm.

(S11) The lens of example S2, wherein the lens is configured to providea visual performance for the eye with a second optical axis, at at leastone visual distance that is at least equivalent to the visualperformance for the eye of a correctly prescribed single-vision lens atthe visual distance, wherein the visual performance is contrastsensitivity and the lens has an aperture size greater than 1.5 mm.

(S12) The lens of examples S1 to S11, wherein the visual Strehl ratio isat least 0.2, 0.22 or 0.24. (S13) The lens of examples S1 to S12,wherein the aberration profile comprises at least four, five or sixspherical aberration terms selected from the group C(4,0) to C(20,0).

Example Set T

(T1) A lens for an eye, the lens comprising: a first optical axis; anaberration profile associated with the first optical axis and having afocal distance; and at least two optical surfaces, wherein the opticalproperties of the lens is characterised upon testing by at least thefollowing properties: three or more higher order aberrations having oneor more of the following components: a primary spherical aberrationC(4,0), a secondary spherical aberration C(6,0), a tertiary sphericalaberration C(8,0), a quaternary spherical aberration C(10,0), apentanary spherical aberration C(12,0), a hexanary spherical aberrationC(14,0), a heptanary spherical aberration C(16,0), an octanary sphericalaberration C(18,0) and a nanonary spherical aberration C(20,0);

the aberration profile when tested on a model eye having a secondoptical axis, with no, or substantially no, aberrations and having alength along the second optical axis equal to, or substantial equal to,the focal distance, results in a retinal image quality (RIQ) of at least0.25, wherein the RIQ is a visual Strehl Ratio that is measured for themodel eye, and is measured substantially along the second optical axisfor at least one pupil diameter in the range 3 mm to 6 mm.

(T2) The lens of the example T1, wherein the visual Strehl ratio ismeasured within a spatial frequency range from one of the following: 10to 20 cycles/degree, 15 to 20 cycles/degree, 15 to 25 cycles/degree, 20to 25 cycles/degree, 20 to 30 cycles/degree, 25 to 30 cycles/degree, 25to 35 cycles/degree, 30 to 35 cycles/degree or 30 to 40 cycles/degreefor a range of wavelengths selected from within the range 380 nm to 800nm inclusive.

(T3) The lens of the example T2, wherein the range of wavelengths isselected from within the range 540 nm to 590 nm inclusive.

(T4) The lens of example T2, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 5° from the second optical axis, or from on-axis to the secondoptical axis to 10° from the second optical axis.

(T5) The lens of example T2, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 5° from the second optical axis, or from on-axis to the secondoptical axis to 15° from the second optical axis.

(T6) The lens of example T3, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 5° from the second optical axis, or from on-axis to the secondoptical axis to 10° from the second optical axis.

(T7) The lens of example T3, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 5° from the second optical axis, or from on-axis to the secondoptical axis to 15° from the second optical axis.

(T8) The lens of example T2, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 10° from the second optical axis, or from on-axis to the secondoptical axis to 20° from the second optical axis.

(T9) The lens of example T3, wherein the visual Strehl ratio is alsomeasured over a field angle of from on-axis to the second optical axisto 10° from the second optical axis, or from on-axis to the secondoptical axis to 20° from the second optical axis.

(T10) The lens of examples T1 to T9, wherein the lens is configured toprovide a visual performance for the eye with a second optical axis, atat least one visual distance that is at least equivalent to the visualperformance for the eye of a correctly prescribed single-vision lens atthe visual distance, wherein the visual performance is visual acuity andthe lens has an aperture size greater than 1.5 mm.

(T11) The lens of example T2, wherein the lens is configured to providea visual performance for the eye with a second optical axis, at at leastone visual distance that is at least equivalent to the visualperformance for the eye of a correctly prescribed single-vision lens atthe visual distance, wherein the visual performance is contrastsensitivity and the lens has an aperture size greater than 1.5 mm.

(T12) The lens of examples T1 to T11, wherein the visual Strehl ratio isat least 0.2, 0.22 or 0.24.

Example Set V

(V1) A contact lens comprising: at least one carrier portion and atleast one optic zone portion; the optic zone comprises a first opticalaxis and an aberration profile associated with the first optical axis;the aberration profile comprises: a focal distance and at least threehigher order aberrations with at least one of a primary sphericalaberration component C(4,0) and a secondary spherical aberrationcomponent C(6,0), wherein the aberration profile provides, for a modeleye, a retinal image quality (RIQ) with a through focus slope thatdegrades in a direction of eye growth and an RIQ of at least 0.3;wherein the model eye has a second optical axis, no aberrations, orsubstantially no aberrations and has an on-axis length equal to, orsubstantially equal to, the focal distance; wherein the RIQ is a visualStrehl Ratio and is measured substantially along the second optical axisfor at least one pupil diameter in the range 3 mm to 6 mm, over aspatial frequency range of 0 to 30 cycles/degree inclusive and for arange of wavelengths from 380 nm to 800 nm inclusive; wherein the lenshas a centroid of the at least one carrier portion and a centroid of theat least one optic zone portion; and wherein the centroid of the opticzone is spaced apart from the centroid of the carrier location by atleast 0.1 mm, 0.3 mm, 0.5 mm or 0.7 mm; and/or the first optical axis isspaced apart from the optic zone centroid by at least 0.1 mm, 0.3 mm,0.5 mm or 0.7 mm; and/or the first optical axis is spaced apart from thecarrier centroid location by at least 0.1 mm, 0.3 mm, 0.5 mm or 0.7 mm.

(V2) The lens of example V1, wherein the lens is a multifocal lens andhas an effective near additional power of at least +1 D.

(V3) The lens of example V1 to V2, wherein the lens is configured toprovide a visual performance over near, intermediate and far distancesthat is at least substantially equivalent to the visual performance of acorrectly prescribed single-vision lens at the far visual distance.

(V4) The lens of example V1 to V3, wherein the lens is configured toprovide minimal ghosting at far, intermediate and near distances.

(V5) The lens of examples V1 to V4, wherein the aberration profilecomprises at least four, five or six spherical aberration terms selectedfrom the group C(4,0) to C(20,0).

Example Set X

(X1) A lens comprising: an optical axis; an optic zone; and a powerprofile associated with the optical axis; wherein the power profile hasa transition between a maxima and a minima, and the maxima is within 0.2mm of the centre of the optic zone and the minima is less than or equalto 0.3, 0.6, 0.9 or 1 mm distance from the maxima; wherein the amplitudeof the transition between the maxima and the minima is at least 2.5D,4D, 5D, or 6D.

(X2) The lens of one of the claims X, wherein the transition between themaxima and the minima is one or more of the following: continuous,discontinuous, monotonic and non-monotonic.

(X3) The lens of one or more of the above X examples, wherein the lensfurther comprises a focal distance; an aberration profile with three ormore higher order aberrations; wherein the aberration profile provides,for a model eye with no aberrations, or substantially no aberrations,and an on-axis length equal to, or substantial equal to, the focaldistance: a retinal image quality (RIQ) with a through focus slope thatdegrades in a direction of eye growth; and a RIQ of at least 0.3 whereinthe RIQ is visual Strehl Ratio measured substantially along the opticalaxis for at least one pupil diameter in the range 3 mm to 6 mm, over aspatial frequency range of 0 to 30 cycles/degree inclusive and at awavelength selected from within the range 540 nm to 590 nm inclusive.

(X4) The lens of one or more of the above X examples, wherein the lensfurther comprises a focal distance; an aberration profile with three ormore higher order aberrations; wherein the aberration profile provides,for a model eye with substantially no aberrations an on-axis lengthequal to, or substantially equal to, the desired focal distance; aretinal image quality (RIQ) with a through focus slope that improves ina direction of eye growth; and a RIQ of at least 0.3; wherein the RIQ ismeasured substantially along the optical axis for at least one pupildiameter in the range 3 mm to 6 mm, over a spatial frequency range of 0to 30 cycles/degree inclusive and at a wavelength selected from withinthe range 540 nm to 590 nm inclusive.

(X5) The lens of one or more of the above X examples, wherein the lensfurther comprises an aberration profile with three or more higher orderaberrations; wherein the aberration profile provides: a focal distancefor a C(2,0) Zernike coefficient term; a peak visual Strehl Ratio(‘first visual Strehl Ratio’) within a through focus range, and a visualStrehl Ratio that remains at or above a second visual Strehl Ratio overthe through focus range that includes said focal distance, wherein thevisual Strehl Ratio is measured for a model eye with no, orsubstantially no, aberration and is measured along the optical axis forat least one pupil diameter in the range 3 mm to 5 mm, over a spatialfrequency range of 0 to 30 cycles/degree inclusive, at a wavelengthselected from within the range 540 nm to 590 nm inclusive, and whereinthe first visual Strehl Ratio is at least 0.35, the second visual StrehlRatio is at least 0.1 and the through focus range is at least 1.8Dioptres

(X6) The lens of one or more of the above X examples, wherein theaberration profile comprises at least four spherical aberration termsselected from the group C(4,0) to C(20,0).

(X7) The lens of one or more of the above X examples, wherein theaberration profile comprises at least five spherical aberration termsselected from the group C(4,0) to C(20,0).

(X8) The lens of one or more of the above X examples, wherein theaberration profile comprises at least six spherical aberration termsselected from the group C(4,0) to C(20,0).

(X9) The lens of one or more of the above X examples, wherein theaberration profile comprises at least seven spherical aberration termsselected from the group C(4,0) to C(20,0).

(X10) The lens of one or more of the above X examples, wherein theaberration profile provides an effective near additional power of atleast 1D; and wherein the lens is configured to provide a visualperformance over intermediate and far distances that is at leastsubstantially equivalent to the visual performance of a correctlyprescribed single-vision lens at the far visual distance; and whereinthe lens is configured to provide minimal ghosting at far, intermediateand near distances.

APPENDIX A Example combinations of spherical aberration Combination C(2,0) C(4,0) C(6,0) C(8,0) C(10,0) C(12,0) C(14,0) C(16,0) C(18,0)C(20,0) No Aberr 0 0 0 0 0 0 0 0 0 0 1 0 −0.125 −0.075 0.000 0.000 0.0000.000 0.000 0.000 0.000 2 0 −0.100 −0.075 0.000 0.000 0.000 0.000 0.0000.000 0.000 3 0 −0.100 −0.025 0.025 0.000 0.000 0.000 0.000 0.000 0.0004 0 −0.100 0.025 0.075 0.025 0.025 0.025 0.025 0.025 0.000 5 0 −0.075−0.075 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6 0 −0.075 −0.025 0.0500.000 −0.025 −0.025 0.000 0.025 0.000 7 0 −0.050 −0.075 0.000 0.0000.000 0.000 0.000 0.000 0.000 8 0 −0.050 −0.050 0.050 0.025 0.000 0.0000.000 0.000 0.000 9 0 −0.050 −0.025 0.050 0.000 −0.025 −0.025 0.0000.025 0.025 10 0 −0.025 −0.075 0.000 0.000 0.000 0.000 0.000 0.000 0.00011 0 −0.025 −0.025 0.050 0.025 −0.025 −0.025 0.000 0.025 0.025 12 00.000 −0.075 0.000 0.000 0.000 0.000 0.000 0.000 0.000 13 0 0.000 −0.0750.050 0.025 0.000 0.025 0.000 −0.025 0.000 14 0 0.000 −0.050 0.000−0.025 −0.025 0.025 0.025 −0.025 −0.025 15 0 0.000 −0.050 0.050 0.025−0.025 −0.025 −0.025 0.000 0.025 16 0 0.000 −0.025 0.075 0.000 −0.0250.025 0.025 0.025 0.025 17 0 0.025 −0.075 0.000 −0.025 −0.025 0.0250.025 0.000 0.000 18 0 0.025 −0.075 0.000 0.000 0.000 0.000 0.000 0.0000.000 19 0 0.025 −0.075 0.025 0.025 −0.025 −0.025 −0.025 0.000 0.025 200 0.025 −0.075 0.050 0.025 −0.025 −0.025 −0.025 0.000 0.000 21 0 0.025−0.050 0.000 0.000 0.000 0.000 0.000 0.000 0.000 22 0 0.025 −0.050 0.0500.000 −0.025 −0.025 0.000 0.025 0.025 23 0 0.025 −0.050 0.050 0.0250.000 0.000 −0.025 −0.025 0.000 24 0 0.025 −0.025 0.075 0.000 −0.0250.025 0.025 0.025 0.025 25 0 0.050 −0.075 0.000 0.000 −0.025 0.000 0.0000.025 0.025 26 0 0.050 −0.075 0.000 0.000 0.000 0.000 0.000 0.000 0.00027 0 0.050 −0.075 0.025 0.025 −0.025 0.000 0.000 −0.025 0.000 28 0 0.050−0.075 0.025 0.025 −0.025 0.000 0.000 0.025 0.025 29 0 0.050 −0.0750.025 0.025 0.000 0.000 −0.025 −0.025 0.000 30 0 0.050 −0.075 0.0250.025 0.000 0.025 0.025 0.025 0.025 31 0 0.050 −0.050 0.000 0.000 0.0000.000 0.000 0.000 0.000 32 0 0.050 −0.025 −0.025 −0.025 −0.025 0.0250.025 0.000 −0.025 33 0 0.050 −0.025 0.075 0.025 −0.025 0.025 0.0250.025 0.025 34 0 0.075 0.050 −0.025 −0.025 0.000 0.000 0.000 0.000 0.00035 0 0.075 −0.075 −0.025 −0.025 0.000 0.025 0.000 0.000 0.000 36 0 0.075−0.075 −0.025 0.000 0.000 0.025 0.025 0.000 0.000 37 0 0.075 −0.0750.000 0.000 −0.025 −0.025 0.000 0.000 0.000 38 0 0.075 −0.075 0.0000.000 −0.025 0.000 0.000 0.000 0.000 39 0 0.075 −0.075 0.000 0.000 0.0000.000 0.000 0.000 0.000 40 0 0.075 −0.075 0.000 0.025 −0.025 −0.0250.000 0.000 0.000 41 0 0.075 −0.075 0.000 0.025 −0.025 0.000 0.000 0.0000.000 42 0 0.075 −0.050 −0.050 −0.025 0.000 0.000 0.025 0.000 −0.025 430 0.075 −0.050 0.000 0.000 0.000 0.000 0.000 0.000 0.000 44 0 0.075−0.025 0.000 0.000 0.000 0.000 0.000 0.000 0.000 45 0 0.075 −0.025 0.0500.000 −0.025 0.025 0.025 0.000 0.000 46 0 0.100 −0.075 −0.050 −0.0250.000 0.025 0.025 −0.025 −0.025 47 0 0.100 −0.075 −0.050 0.000 0.0000.025 0.025 −0.025 −0.025 48 0 0.100 −0.075 −0.025 0.000 0.000 0.0000.000 0.000 0.000 49 0 0.100 −0.075 −0.025 0.000 0.000 0.025 0.000 0.0000.000 50 0 0.100 −0.075 0.000 0.000 0.000 0.000 0.000 0.000 0.000 51 00.100 −0.075 0.000 0.025 −0.025 −0.025 0.025 0.025 0.000 52 0 0.100−0.050 −0.050 −0.025 0.000 −0.025 −0.025 −0.025 −0.025 53 0 0.100 −0.050−0.025 −0.025 −0.025 0.025 0.000 −0.025 0.000 54 0 0.100 −0.050 0.0000.000 0.000 0.000 0.000 0.000 0.000 55 0 0.100 −0.050 0.000 0.000 0.0000.025 0.025 0.000 0.000 56 0 0.100 −0.050 0.000 0.000 0.000 0.025 0.0250.025 0.025 57 0 0.100 −0.050 0.000 0.025 0.025 0.000 −0.025 −0.025−0.025 58 0 0.100 −0.025 0.000 0.000 0.000 0.000 0.000 0.000 0.000 59 00.100 −0.025 0.000 0.025 0.025 0.000 −0.025 −0.025 −0.025 60 0 0.100−0.025 0.025 −0.025 −0.025 0.025 0.025 0.000 0.000 61 0 0.100 0.0000.000 −0.025 0.000 0.025 0.000 0.000 0.025 62 0 0.100 0.000 0.000 0.0000.000 0.000 0.000 0.000 0.000 63 0 0.100 0.000 0.050 0.000 −0.025 0.0250.000 −0.025 0.000 64 0 0.125 −0.075 −0.075 −0.025 0.000 0.025 0.025−0.025 −0.025 65 0 0.125 −0.075 −0.075 0.000 0.000 0.000 0.000 0.0000.000 66 0 0.125 −0.075 0.000 0.000 0.000 0.000 0.000 0.000 0.000 67 00.125 −0.050 −0.025 −0.025 −0.025 0.000 0.000 0.000 0.000 68 0 0.125−0.050 −0.025 −0.025 −0.025 0.025 0.000 0.000 0.000 69 0 0.125 −0.050−0.025 0.000 0.000 0.025 0.025 0.000 0.000 70 0 0.125 −0.050 0.000 0.0000.000 0.000 0.000 0.000 0.000 71 0 0.125 −0.050 0.000 0.025 0.025 0.0250.000 0.000 0.000 72 0 0.125 −0.025 0.000 −0.025 −0.025 0.000 0.000−0.025 −0.025 73 0 0.125 −0.025 0.000 0.000 0.000 0.000 0.000 0.0000.000 74 0 0.125 −0.025 0.025 0.000 −0.025 0.000 0.000 0.000 0.000 75 00.125 −0.025 0.025 0.000 0.000 0.025 0.025 0.000 0.000 76 0 0.125 −0.0250.025 0.025 0.025 −0.025 0.025 0.025 0.025 77 0 0.125 0.000 0.000 0.0000.000 0.000 0.000 0.000 0.000 78 0 0.125 0.000 0.025 −0.025 −0.025 0.0250.000 −0.025 −0.025

APPENDIX B Through focus RIQ for combinations of spherical aberration inAppendix A Combination −1.50 −1.25 −1.00 −0.75 −0.50 −0.25 0.00 0.250.50 0.75 1.00 1.25 1.50 No Aberr 0.024 0.040 0.073 0.148 0.307 0.7091.000 0.709 0.307 0.148 0.073 0.040 0.024 1 0.089 0.135 0.192 0.2430.304 0.434 0.606 0.667 0.542 0.329 0.152 0.056 0.021 2 0.084 0.1310.196 0.265 0.346 0.482 0.643 0.676 0.514 0.281 0.113 0.036 0.012 30.028 0.053 0.115 0.258 0.473 0.628 0.648 0.595 0.479 0.310 0.161 0.0710.028 4 0.039 0.067 0.153 0.313 0.458 0.493 0.477 0.492 0.470 0.3610.220 0.112 0.052 5 0.082 0.128 0.198 0.281 0.384 0.532 0.675 0.6750.481 0.236 0.080 0.021 0.006 6 0.100 0.129 0.157 0.246 0.402 0.5140.542 0.559 0.515 0.338 0.146 0.051 0.024 7 0.083 0.129 0.199 0.2890.412 0.576 0.704 0.666 0.445 0.196 0.054 0.010 0.002 8 0.069 0.1050.176 0.305 0.479 0.603 0.614 0.565 0.454 0.262 0.099 0.030 0.010 90.124 0.168 0.181 0.212 0.338 0.502 0.579 0.579 0.508 0.319 0.117 0.0270.016 10 0.089 0.133 0.201 0.293 0.425 0.607 0.730 0.656 0.409 0.1610.034 0.003 0.001 11 0.104 0.159 0.199 0.247 0.359 0.508 0.581 0.5700.502 0.326 0.125 0.035 0.023 12 0.098 0.141 0.206 0.293 0.423 0.6180.749 0.649 0.377 0.134 0.021 0.001 0.002 13 0.157 0.206 0.250 0.2820.354 0.482 0.542 0.480 0.364 0.232 0.120 0.060 0.032 14 0.092 0.1840.314 0.371 0.390 0.505 0.592 0.481 0.297 0.204 0.161 0.097 0.041 150.153 0.215 0.247 0.261 0.324 0.453 0.533 0.514 0.447 0.307 0.129 0.0380.025 16 0.152 0.207 0.237 0.260 0.363 0.509 0.531 0.442 0.363 0.2650.137 0.056 0.029 17 0.158 0.218 0.286 0.308 0.324 0.457 0.611 0.5640.352 0.181 0.101 0.048 0.011 18 0.111 0.152 0.213 0.293 0.410 0.6040.754 0.650 0.356 0.113 0.013 0.004 0.004 19 0.168 0.205 0.235 0.2850.367 0.476 0.539 0.482 0.365 0.253 0.138 0.052 0.023 20 0.161 0.2020.237 0.282 0.361 0.468 0.518 0.465 0.378 0.267 0.124 0.038 0.019 210.081 0.116 0.174 0.255 0.405 0.680 0.878 0.715 0.342 0.093 0.015 0.0020.001 22 0.151 0.212 0.253 0.256 0.304 0.463 0.584 0.514 0.360 0.2230.095 0.016 0.003 23 0.153 0.205 0.242 0.255 0.316 0.493 0.638 0.5630.363 0.201 0.096 0.041 0.023 24 0.159 0.214 0.250 0.256 0.322 0.4760.548 0.465 0.357 0.251 0.127 0.046 0.021 25 0.158 0.201 0.231 0.2530.312 0.472 0.648 0.612 0.359 0.141 0.075 0.067 0.043 26 0.126 0.1660.222 0.293 0.388 0.567 0.739 0.657 0.350 0.099 0.008 0.005 0.006 270.161 0.203 0.236 0.253 0.304 0.475 0.648 0.593 0.370 0.190 0.091 0.0390.015 28 0.164 0.201 0.226 0.253 0.323 0.472 0.604 0.547 0.352 0.1970.112 0.058 0.031 29 0.171 0.206 0.240 0.274 0.328 0.463 0.608 0.5640.362 0.193 0.094 0.036 0.012 30 0.171 0.206 0.231 0.259 0.326 0.4750.626 0.589 0.363 0.150 0.057 0.031 0.015 31 0.097 0.135 0.192 0.2680.389 0.628 0.848 0.728 0.347 0.078 0.006 0.001 0.003 32 0.074 0.1340.238 0.370 0.462 0.553 0.624 0.516 0.286 0.156 0.129 0.096 0.052 330.159 0.212 0.245 0.251 0.305 0.461 0.564 0.496 0.375 0.264 0.138 0.0480.019 34 0.022 0.044 0.114 0.279 0.496 0.623 0.634 0.591 0.479 0.3100.160 0.069 0.030 35 0.161 0.200 0.244 0.318 0.404 0.493 0.584 0.5500.352 0.162 0.072 0.032 0.009 36 0.151 0.217 0.289 0.353 0.390 0.4550.568 0.563 0.373 0.173 0.080 0.042 0.013 37 0.151 0.206 0.264 0.3040.336 0.450 0.630 0.628 0.372 0.127 0.038 0.014 0.004 38 0.164 0.2110.254 0.279 0.309 0.455 0.681 0.686 0.400 0.126 0.027 0.011 0.005 390.142 0.181 0.232 0.292 0.364 0.512 0.699 0.664 0.364 0.097 0.005 0.0060.008 40 0.155 0.222 0.286 0.331 0.369 0.465 0.601 0.579 0.365 0.1720.085 0.037 0.008 41 0.151 0.204 0.251 0.282 0.320 0.459 0.601 0.5790.365 0.172 0.085 0.037 0.008 42 0.118 0.171 0.252 0.367 0.460 0.5060.539 0.496 0.329 0.166 0.098 0.069 0.036 43 0.115 0.156 0.212 0.2830.376 0.563 0.784 0.729 0.371 0.080 0.001 0.003 0.005 44 0.086 0.1260.186 0.272 0.392 0.602 0.826 0.761 0.391 0.094 0.012 0.005 0.001 450.153 0.203 0.257 0.284 0.316 0.452 0.609 0.566 0.367 0.207 0.104 0.0350.011 46 0.180 0.256 0.316 0.408 0.497 0.493 0.427 0.336 0.212 0.1220.109 0.104 0.064 47 0.171 0.253 0.325 0.407 0.458 0.443 0.429 0.4000.289 0.173 0.131 0.112 0.066 48 0.151 0.211 0.281 0.358 0.417 0.4700.566 0.585 0.397 0.155 0.035 0.004 0.004 49 0.155 0.203 0.255 0.3300.407 0.472 0.560 0.561 0.375 0.168 0.075 0.042 0.018 50 0.159 0.1970.240 0.289 0.339 0.449 0.636 0.663 0.396 0.110 0.005 0.007 0.009 510.185 0.272 0.360 0.392 0.353 0.357 0.461 0.486 0.330 0.168 0.108 0.0770.037 52 0.096 0.141 0.222 0.351 0.472 0.508 0.515 0.524 0.412 0.1960.057 0.024 0.021 53 0.158 0.206 0.242 0.306 0.392 0.462 0.534 0.5330.381 0.208 0.116 0.063 0.025 54 0.134 0.177 0.231 0.296 0.365 0.4940.694 0.710 0.409 0.101 0.001 0.004 0.007 55 0.152 0.204 0.259 0.3160.366 0.464 0.626 0.630 0.369 0.110 0.031 0.028 0.016 56 0.161 0.2070.253 0.290 0.338 0.458 0.619 0.607 0.360 0.117 0.033 0.027 0.022 570.143 0.197 0.268 0.357 0.426 0.471 0.522 0.486 0.298 0.128 0.086 0.0780.044 58 0.105 0.151 0.214 0.299 0.398 0.542 0.721 0.717 0.423 0.1230.017 0.003 0.003 59 0.110 0.169 0.259 0.371 0.457 0.518 0.571 0.5150.302 0.113 0.068 0.073 0.053 60 0.158 0.202 0.246 0.308 0.374 0.4550.553 0.536 0.366 0.196 0.093 0.030 0.008 61 0.118 0.160 0.205 0.2840.407 0.520 0.588 0.569 0.421 0.224 0.088 0.026 0.007 62 0.076 0.1190.189 0.297 0.437 0.593 0.722 0.683 0.425 0.165 0.053 0.021 0.006 630.156 0.207 0.243 0.258 0.318 0.460 0.563 0.511 0.364 0.236 0.140 0.0750.044 64 0.194 0.280 0.335 0.402 0.502 0.516 0.402 0.272 0.179 0.1240.113 0.113 0.086 65 0.155 0.251 0.353 0.432 0.463 0.418 0.355 0.3680.387 0.303 0.163 0.062 0.021 66 0.175 0.210 0.246 0.284 0.316 0.3850.554 0.643 0.439 0.141 0.009 0.008 0.010 67 0.163 0.214 0.265 0.3280.402 0.466 0.529 0.536 0.389 0.186 0.072 0.031 0.009 68 0.163 0.2010.232 0.294 0.397 0.476 0.522 0.506 0.365 0.192 0.103 0.062 0.031 690.157 0.220 0.281 0.355 0.428 0.468 0.519 0.533 0.375 0.160 0.065 0.0500.032 70 0.153 0.198 0.248 0.304 0.354 0.431 0.590 0.664 0.449 0.1430.010 0.005 0.008 71 0.153 0.201 0.261 0.343 0.412 0.458 0.535 0.5520.372 0.143 0.051 0.040 0.024 72 0.151 0.207 0.259 0.316 0.391 0.4660.517 0.487 0.353 0.210 0.114 0.042 0.006 73 0.126 0.176 0.241 0.3200.401 0.489 0.609 0.645 0.446 0.168 0.033 0.005 0.004 74 0.161 0.2030.237 0.270 0.333 0.456 0.608 0.618 0.406 0.179 0.081 0.038 0.010 750.159 0.202 0.243 0.289 0.349 0.456 0.592 0.584 0.367 0.145 0.046 0.0100.003 76 0.076 0.148 0.260 0.351 0.375 0.411 0.515 0.518 0.321 0.1340.082 0.053 0.008 77 0.096 0.147 0.224 0.329 0.451 0.554 0.619 0.5950.422 0.202 0.074 0.027 0.007 78 0.160 0.216 0.272 0.318 0.372 0.4340.455 0.411 0.344 0.276 0.169 0.060 0.018

APPENDIX C Example combinations of spherical aberration Combination C(2,0) C(4,0) C(6,0) C(8,0) C(10,0) C(12,0) C(14,0) C(16,0) C(18,0)C(20,0) No Aberr 0 0 0 0 0 0 0 0 0 0 101 0 −0.125 −0.075 0.000 0.025−0.025 −0.025 0.025 0.000 −0.025 102 0 −0.125 −0.050 0.000 0.025 0.000−0.025 0.025 0.000 −0.025 103 0 −0.125 −0.050 0.000 0.025 0.000 −0.0250.025 0.025 −0.025 104 0 −0.125 −0.050 0.025 0.025 −0.025 −0.025 0.0250.000 −0.025 105 0 −0.125 −0.050 0.050 0.025 −0.025 0.000 0.025 −0.025−0.025 106 0 −0.125 −0.050 0.050 0.025 −0.025 0.025 0.000 0.000 0.025107 0 −0.125 −0.025 −0.025 0.025 0.025 −0.025 0.000 0.025 0.000 108 0−0.125 −0.025 0.000 0.000 0.025 −0.025 −0.025 0.025 0.025 109 0 −0.125−0.025 0.000 0.000 0.025 0.000 −0.025 0.025 0.025 110 0 −0.125 −0.0250.000 0.025 0.025 −0.025 −0.025 0.025 0.000 111 0 −0.125 −0.025 0.0000.025 0.025 −0.025 0.000 0.025 0.000 112 0 −0.125 −0.025 0.000 0.0250.025 −0.025 0.025 0.025 0.000 113 0 −0.125 −0.025 0.025 0.025 0.000−0.025 0.025 0.025 −0.025 114 0 −0.125 −0.025 0.075 0.025 −0.025 0.0250.000 0.000 0.025 115 0 −0.125 0.000 0.050 0.025 0.000 −0.025 0.0250.025 −0.025 116 0 −0.125 0.000 0.075 0.025 −0.025 −0.025 0.025 0.000−0.025 117 0 −0.125 0.050 0.075 0.025 0.025 0.000 0.000 0.000 −0.025 1180 −0.125 0.075 0.075 −0.025 0.000 −0.025 −0.025 0.000 0.000 119 0 −0.100−0.075 −0.050 0.025 0.025 −0.025 −0.025 0.025 0.025 120 0 −0.100 −0.050−0.050 0.025 0.025 −0.025 −0.025 0.025 0.025 121 0 −0.100 −0.050 −0.0250.025 0.025 −0.025 −0.025 0.025 0.025 122 0 −0.100 −0.025 −0.050 0.0250.025 −0.025 −0.025 0.025 0.000 123 0 −0.100 −0.025 −0.025 0.000 0.025−0.025 −0.025 0.025 0.025 124 0 −0.100 −0.025 −0.025 0.025 0.025 −0.025−0.025 0.025 0.000 125 0 −0.100 0.050 0.075 −0.025 −0.025 −0.025 −0.025−0.025 0.000 126 0 −0.100 0.075 0.075 −0.025 0.000 −0.025 −0.025 0.0000.000 127 0 −0.100 0.075 0.075 0.000 0.000 −0.025 −0.025 −0.025 −0.025128 0 −0.100 0.075 0.075 0.000 0.000 −0.025 −0.025 0.000 −0.025 129 0−0.075 0.025 0.075 0.025 −0.025 −0.025 0.025 −0.025 −0.025 130 0 −0.0750.050 0.075 −0.025 −0.025 0.000 −0.025 0.000 0.025 131 0 −0.075 0.0500.075 −0.025 −0.025 0.025 0.000 0.025 0.025 132 0 −0.075 0.050 0.0750.025 −0.025 −0.025 0.000 −0.025 −0.025 133 0 −0.075 0.050 0.075 0.0250.000 −0.025 0.025 0.000 −0.025 134 0 −0.075 0.075 0.075 −0.025 −0.025−0.025 −0.025 0.000 0.000 135 0 −0.075 0.075 0.075 −0.025 −0.025 −0.025−0.025 0.000 0.025 136 0 −0.075 0.075 0.075 −0.025 −0.025 0.000 −0.0250.025 0.025 137 0 −0.075 0.075 0.075 −0.025 −0.025 0.000 0.000 0.0000.025 138 0 −0.075 0.075 0.075 −0.025 −0.025 0.025 0.000 0.000 0.025 1390 −0.075 0.075 0.075 −0.025 −0.025 0.025 0.000 0.025 0.025 140 0 −0.050−0.050 −0.075 0.025 0.025 −0.025 0.000 0.000 0.000 141 0 −0.050 0.0500.075 −0.025 −0.025 0.000 −0.025 0.000 0.025 142 0 −0.050 0.050 0.075−0.025 −0.025 0.000 −0.025 0.025 0.025 143 0 −0.050 0.050 0.075 0.025−0.025 −0.025 0.025 −0.025 −0.025 144 0 −0.050 0.075 0.075 −0.025 −0.025−0.025 −0.025 0.025 0.025 145 0 −0.050 0.075 0.075 −0.025 −0.025 0.0250.000 0.000 0.025 146 0 −0.050 0.075 0.075 −0.025 −0.025 0.025 0.0000.025 0.025 147 0 −0.025 0.075 0.075 −0.025 −0.025 0.025 0.000 0.0000.025 148 0 −0.025 0.075 0.075 −0.025 −0.025 0.025 0.000 0.025 0.025 1490 0.000 0.075 0.075 −0.025 −0.025 0.025 0.000 0.000 0.025 150 0 0.0000.075 0.075 −0.025 −0.025 0.025 0.000 0.025 0.025 151 0 0.025 −0.050−0.075 0.025 0.025 0.025 0.025 −0.025 −0.025 152 0 0.050 0.075 −0.050−0.025 0.025 −0.025 −0.025 −0.025 −0.025 153 0 0.075 0.075 −0.050 0.0000.025 −0.025 −0.025 −0.025 −0.025 154 0 0.100 0.050 −0.075 −0.025 0.000−0.025 0.025 0.000 0.000 155 0 0.100 0.050 −0.075 −0.025 0.025 0.0000.025 0.000 −0.025 156 0 0.100 0.050 −0.075 −0.025 0.025 0.025 0.0250.025 0.000 157 0 0.100 0.050 −0.075 0.000 0.025 0.000 0.000 −0.025−0.025 158 0 0.100 0.075 −0.075 −0.025 0.000 −0.025 0.000 0.000 0.000159 0 0.100 0.075 −0.075 −0.025 0.025 0.000 0.025 0.025 0.000 160 00.100 0.075 −0.075 −0.025 0.025 0.025 0.025 0.025 0.025 161 0 0.1250.050 −0.075 0.000 −0.025 −0.025 0.000 0.000 0.000 162 0 0.125 0.075−0.075 −0.025 0.000 −0.025 −0.025 0.000 0.000 163 0 0.125 0.075 −0.075−0.025 0.000 −0.025 0.000 0.000 0.000 164 0 0.125 0.075 −0.050 0.0000.000 −0.025 0.000 −0.025 −0.025 165 0 0.125 0.075 −0.050 0.000 0.000−0.025 0.000 −0.025 0.000 166 0 0.125 0.075 −0.050 0.000 0.000 −0.0250.000 0.000 0.000 167 0 0.125 0.075 −0.050 0.000 0.000 −0.025 0.0000.025 0.025

APPENDIX D Through focus RIQ for combinations of spherical aberration inAppendix C Combination −1.50 −1.25 −1.00 −0.75 −0.50 −0.25 0.00 0.250.50 0.75 1.00 1.25 1.50 No Aberr 0.024 0.040 0.073 0.148 0.307 0.7091.000 0.709 0.307 0.148 0.073 0.040 0.024 101 0.071 0.102 0.206 0.3710.466 0.446 0.409 0.397 0.365 0.305 0.236 0.171 0.114 102 0.075 0.1130.213 0.357 0.421 0.407 0.430 0.459 0.402 0.301 0.220 0.160 0.110 1030.071 0.106 0.224 0.382 0.431 0.388 0.385 0.405 0.374 0.309 0.238 0.1730.120 104 0.045 0.079 0.216 0.430 0.524 0.446 0.376 0.385 0.383 0.3260.240 0.161 0.106 105 0.043 0.075 0.203 0.427 0.551 0.478 0.377 0.3550.350 0.314 0.242 0.160 0.101 106 0.045 0.108 0.230 0.382 0.459 0.4130.366 0.386 0.382 0.312 0.221 0.151 0.109 107 0.032 0.091 0.212 0.3230.360 0.391 0.463 0.483 0.407 0.317 0.255 0.198 0.141 108 0.044 0.1090.239 0.330 0.354 0.389 0.444 0.462 0.422 0.347 0.264 0.183 0.111 1090.029 0.106 0.231 0.314 0.358 0.427 0.489 0.478 0.403 0.321 0.251 0.1760.107 110 0.028 0.098 0.234 0.343 0.359 0.364 0.439 0.503 0.447 0.3240.232 0.168 0.109 111 0.033 0.093 0.221 0.343 0.385 0.402 0.469 0.5140.446 0.326 0.234 0.168 0.113 112 0.049 0.091 0.202 0.327 0.384 0.4050.450 0.467 0.400 0.303 0.223 0.163 0.116 113 0.048 0.082 0.211 0.4000.476 0.408 0.365 0.391 0.387 0.325 0.239 0.167 0.118 114 0.044 0.0950.211 0.386 0.486 0.426 0.358 0.375 0.370 0.305 0.231 0.167 0.119 1150.053 0.096 0.212 0.360 0.420 0.374 0.361 0.416 0.420 0.340 0.239 0.1640.119 116 0.067 0.121 0.220 0.342 0.392 0.355 0.361 0.434 0.455 0.3890.277 0.169 0.101 117 0.039 0.095 0.206 0.321 0.369 0.365 0.383 0.4220.418 0.358 0.268 0.180 0.120 118 0.061 0.120 0.212 0.315 0.388 0.3870.350 0.353 0.365 0.344 0.304 0.244 0.168 119 0.065 0.127 0.213 0.3090.364 0.393 0.432 0.436 0.395 0.342 0.269 0.183 0.111 120 0.040 0.0980.211 0.322 0.354 0.366 0.412 0.425 0.391 0.355 0.296 0.204 0.125 1210.039 0.104 0.236 0.352 0.374 0.383 0.441 0.469 0.426 0.351 0.264 0.1730.102 122 0.028 0.085 0.205 0.324 0.362 0.371 0.405 0.413 0.372 0.3220.267 0.194 0.125 123 0.039 0.083 0.201 0.313 0.367 0.431 0.486 0.4580.392 0.348 0.288 0.192 0.105 124 0.020 0.075 0.204 0.339 0.396 0.4170.452 0.459 0.403 0.317 0.242 0.172 0.107 125 0.044 0.096 0.203 0.3270.395 0.383 0.359 0.389 0.423 0.393 0.304 0.194 0.101 126 0.057 0.1060.205 0.327 0.410 0.411 0.368 0.358 0.369 0.346 0.293 0.224 0.147 1270.038 0.087 0.200 0.338 0.402 0.383 0.367 0.388 0.397 0.359 0.282 0.1940.123 128 0.037 0.097 0.206 0.319 0.378 0.380 0.379 0.396 0.381 0.3190.250 0.188 0.134 129 0.053 0.097 0.219 0.353 0.404 0.378 0.365 0.3970.395 0.323 0.235 0.163 0.112 130 0.050 0.106 0.211 0.342 0.446 0.4740.421 0.381 0.381 0.347 0.267 0.179 0.109 131 0.058 0.121 0.201 0.3020.420 0.465 0.419 0.397 0.393 0.330 0.238 0.161 0.104 132 0.025 0.0820.215 0.346 0.385 0.372 0.406 0.470 0.463 0.365 0.248 0.158 0.104 1330.059 0.103 0.205 0.318 0.370 0.369 0.394 0.451 0.437 0.328 0.219 0.1510.109 134 0.045 0.095 0.210 0.336 0.389 0.380 0.383 0.424 0.441 0.3880.295 0.199 0.116 135 0.046 0.094 0.209 0.331 0.379 0.374 0.371 0.3920.413 0.383 0.303 0.207 0.121 136 0.048 0.102 0.208 0.326 0.393 0.3910.358 0.355 0.377 0.356 0.289 0.213 0.142 137 0.028 0.082 0.201 0.3250.378 0.368 0.367 0.418 0.461 0.422 0.319 0.200 0.103 138 0.024 0.0830.205 0.344 0.424 0.411 0.371 0.380 0.404 0.376 0.299 0.206 0.126 1390.036 0.107 0.214 0.316 0.387 0.398 0.373 0.388 0.408 0.363 0.278 0.1910.120 140 0.067 0.117 0.201 0.311 0.384 0.416 0.461 0.485 0.422 0.3120.219 0.151 0.102 141 0.055 0.105 0.215 0.361 0.464 0.483 0.431 0.3790.364 0.333 0.256 0.169 0.101 142 0.075 0.131 0.218 0.317 0.399 0.4380.415 0.382 0.374 0.331 0.245 0.168 0.110 143 0.052 0.090 0.204 0.3500.411 0.382 0.371 0.406 0.398 0.313 0.222 0.161 0.118 144 0.078 0.1180.208 0.319 0.381 0.398 0.405 0.407 0.399 0.353 0.273 0.194 0.124 1450.028 0.086 0.212 0.359 0.437 0.421 0.381 0.386 0.403 0.368 0.286 0.1920.116 146 0.036 0.105 0.226 0.341 0.402 0.405 0.382 0.390 0.405 0.3600.269 0.179 0.109 147 0.035 0.092 0.218 0.372 0.454 0.434 0.387 0.3830.391 0.352 0.272 0.183 0.111 148 0.042 0.104 0.231 0.363 0.423 0.4150.388 0.386 0.392 0.348 0.260 0.171 0.104 149 0.046 0.102 0.223 0.3810.471 0.449 0.391 0.374 0.371 0.329 0.255 0.177 0.110 150 0.053 0.1070.230 0.378 0.449 0.430 0.391 0.375 0.370 0.328 0.249 0.168 0.104 1510.087 0.139 0.218 0.318 0.389 0.428 0.447 0.425 0.379 0.315 0.228 0.1500.103 152 0.048 0.099 0.206 0.320 0.374 0.384 0.417 0.463 0.443 0.3360.220 0.154 0.125 153 0.042 0.095 0.205 0.324 0.375 0.387 0.427 0.4660.430 0.318 0.209 0.153 0.130 154 0.075 0.124 0.201 0.316 0.436 0.4540.387 0.368 0.367 0.303 0.217 0.152 0.104 155 0.072 0.118 0.205 0.3480.488 0.481 0.376 0.359 0.381 0.320 0.222 0.157 0.118 156 0.040 0.0960.200 0.357 0.504 0.508 0.407 0.366 0.363 0.301 0.213 0.155 0.119 1570.047 0.097 0.202 0.355 0.455 0.420 0.357 0.393 0.426 0.345 0.223 0.1560.132 158 0.053 0.110 0.206 0.316 0.403 0.413 0.369 0.385 0.428 0.3850.276 0.183 0.122 159 0.071 0.127 0.209 0.315 0.415 0.418 0.355 0.3700.417 0.368 0.260 0.175 0.126 160 0.050 0.107 0.206 0.329 0.429 0.4290.363 0.363 0.389 0.335 0.236 0.164 0.125 161 0.056 0.121 0.211 0.3040.386 0.420 0.400 0.393 0.387 0.319 0.226 0.161 0.121 162 0.055 0.1220.222 0.313 0.355 0.361 0.363 0.401 0.449 0.410 0.285 0.170 0.107 1630.063 0.129 0.233 0.335 0.403 0.411 0.363 0.354 0.400 0.387 0.291 0.1890.118 164 0.062 0.106 0.202 0.330 0.412 0.421 0.394 0.375 0.371 0.3480.275 0.177 0.105 165 0.050 0.107 0.217 0.345 0.423 0.426 0.379 0.3510.361 0.332 0.240 0.151 0.101 166 0.047 0.105 0.201 0.312 0.411 0.4590.438 0.418 0.420 0.366 0.262 0.173 0.112 167 0.053 0.119 0.210 0.3070.405 0.466 0.447 0.416 0.394 0.311 0.212 0.161 0.122

1. A lens for an eye, the lens comprising: an optical axis; anaberration profile about the optical axis and having a focal distance;and at least two optical surfaces; wherein the lens's optical propertiescan be characterised upon testing by at least the following properties:two or more higher order aberrations having one or more of the followingcomponents: a primary spherical aberration C(4,0), a secondary sphericalaberration C(6,0), a tertiary spherical aberration C(8,0), a quaternaryspherical aberration C(10,0), a pentanary spherical aberration C(12,0),a hexanary spherical aberration C(14,0), a heptanary sphericalaberration C(16,0), an octanary spherical aberration C(18,0) and ananonary spherical aberration C(20,0); and wherein the aberrationprofile when tested on a model eye with no, or substantially no,aberrations and having an on-axis length equal, or substantially equal,to the focal distance, results in a retinal image quality (RIQ) with athrough focus slope so that the RIQ decreases in a direction of eyegrowth, where the RIQ is determined by a visual Strehl Ratio that ismeasured substantially along the optical axis; and the RIQ is measuredfor a model eye with no, or substantially no, aberration and is measuredalong the optical axis for at least one pupil diameter in the range 3 mmto 5 mm, over a spatial frequency range of 0 to 30 cycles/degreeinclusive, at a wavelength selected from within the range 540 nm to 590nm inclusive.
 2. A lens for an eye, the lens comprising: an opticalaxis; an aberration profile about the optical axis and having a focaldistance; at least two optical surfaces; wherein the lens's opticalproperties can be characterised upon testing by at least the followingproperties: two or more higher order aberrations having one or more ofthe following components: a primary spherical aberration C(4,0), asecondary spherical aberration C(6,0), a tertiary spherical aberrationC(8,0), a quaternary spherical aberration C(10,0), a pentanary sphericalaberration C(12,0), a hexanary spherical aberration C(14,0), a heptanaryspherical aberration C(16,0), an octanary spherical aberration C(18,0)and a nanonary spherical aberration C(20,0); the aberration profile whentested on a model eye with no, or substantially no, aberrations andhaving an on-axis length equal, or substantially equal, to the focaldistance, results in a through focus RIQ, within the through focusrange, a first RIQ which is a peak RIQ and that remains at or above asecond RIQ over the through focus range that includes the focaldistance; and the first and second RIQs are measured for a model eyewith no, or substantially no, aberration and is measured along theoptical axis for at least one pupil diameter in the range 3 mm to 5 mm,over a spatial frequency range of 0 to 30 cycles/degree inclusive, at awavelength selected from within the range 540 nm to 590 nm inclusive. 3.The lens of claim 1, wherein the lens is further characterised byminimal ghosting at near, intermediate and far distances.
 4. The lens ofclaim 1, wherein the lens is further configured to provide the RIQ of atleast 0.1 in the near distance range, the RIQ of at least 0.27 in theintermediate distance range and the RIQ of at least 0.35 in the fardistance range.
 5. The lens of claim 1, wherein the lens is furtherconfigured to provide two or more of the following: the RIQ of at least0.1 in the near distance range, the RIQ of at least 0.27 in theintermediate distance range and the RIQ of at least 0.35 in the fardistance range.
 6. The lens of claim 1, wherein the slope averaged overa horizontal field of at least −20° to +20° degrades in a direction ofeye growth.
 7. The lens of claim 1, wherein the slope averaged over ahorizontal field of at least −20° to +20° improves in a direction of eyegrowth.
 8. The lens of claim 1, wherein the slope averaged over avertical field of at least −20° to +20° degrades in a direction of eyegrowth.
 9. The lens of claim 1, wherein the slope averaged over avertical field of at least −20° to +20° improves in a direction of eyegrowth.
 10. The lens of claim 1, wherein the aberration profile providesthe RIQ with a through focus slope that degrades in a direction of eyegrowth when primary or secondary astigmatism is added to the aberrationprofile.
 11. The lens of claim 1, wherein the primary or secondaryastigmatism is added to the desired aberration profile by altering oneor more of the following terms: C(2,−2), C(2,2), C(4,−2), C(4,2),C(6,−2) and/or C(6,2).
 12. The lens of claim 1, wherein the RIQ ischaracterised by ${R\; I\; Q} = \frac{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( {{real}( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{W( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) )} )\end{matrix}}{\begin{matrix}{\int{{\int_{- {Fmin}}^{+ {Fmax}}{C\; S\; {F( {x,\; y} )}*}}\;}} \\( ( ( {F\; {T( \; {{F\; T\; \{ {{A( {\rho,\; \theta} )}*{\exp \lbrack {\frac{2\; \pi \; i}{\lambda}*{{Wdiff}( {\rho,\; \theta} )}} \rbrack}} \}}}^{2} )}} ) ) )\end{matrix}}$ wherein: Fmin is 0 cycles/degree and Fmax is 30cycles/degree; CSF(x, y) denotes the contrast sensitivity function CSF(F)=2.6(0.0192+0.114f)e^(−(0.114f)̂1.1), where f specifies the testedspatial frequency, in the range of F_(min) to F_(max); FT denotes a 2Dfast Fourier transform; A (ρ, θ) denotes the pupil amplitude functionacross the pupil diameter; W (ρ, θ) denotes wavefront of the test casemeasured for i=1 to 20W(ρ,θ)=Σ_(i=1) ^(k) a _(i) Z _(i)(ρ,θ); Wdiff (ρ, θ) denotes wavefrontof the diffraction limited case; ρ and θ are normalised polarcoordinates, where ρ represents the radial coordinate and θ representsthe angular coordinate or azimuth; and λ denotes wavelength.
 13. Thelens of claim 2, wherein the first visual Strehl Ratio is at least 0.3.14. The lens of claim 2, wherein the second visual Strehl Ratio is atleast 0.1.
 15. The lens of claim 2, wherein the through focus range isat least 1.7 D.
 16. The lens of claim 1, wherein a power profile isassociated with the optical axis and the power profile has a transitionbetween a maxima and a minima, and the maxima is within 0.2 mm of thecentre of the optic zone and the minima is less than or equal to 0.3 mmdistance from the maxima; wherein the amplitude of the transitionbetween the maxima and the minima is at least 2.5D.
 17. The lens ofclaim 16, wherein the transition between the maxima and the minima isone or more of the following: continuous, discontinuous, monotonic andnon-monotonic.
 18. A multifocal lens comprising: an optical axis; aneffective near additional power of at least 1 D; the optical propertiesof the multifocal lens are configured with an aberration profileassociated with the optical axis; the aberration profile is comprised ofa defocus term and at least two spherical aberration terms; themultifocal lens is configured to provide a visual performance overintermediate and far distances that is at least substantially equivalentto the visual performance of a correctly prescribed single-vision lensat the far visual distance and the lens is configured to provide minimalghosting at far, intermediate and near distances.
 19. The multifocallens of claim 18, wherein the lens is configured to provide near visualacuity of at least 6/6 in individuals that can achieve 6/6 visualacuity.
 20. The multifocal lens of claim 18, wherein the lens isconfigured to provide at least acceptable visual performance at neardistances.